The answer is simple if you understand that there is a number y always between 3 and x, but NEVER equal to either x > y > 3 In the Real or Rational numbers, no matter how close x is to 3, there is a way to slip a y "in between x and 3θ = Angle between two radii R = Radius of outer circle r = Radius of inner circle θ = Angle between two radii R = Radius of outer circle r = Radius of inner circle 6 Statistics Formulas Mean am = a1 a2a3 a4 4 = n ∑ 0a n a m = a 1 a 2 a 3 a 4 4 = ∑ 0 n a nQuestion The equation x3 3xy y3 = 1 is solved in integers Find the possible values of xy Found 3 solutions by Alan3354, Edwin McCravy, richard1234
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X^3+y^3+z^3=(x+y)^3-3xy(x+y)+z^3-Let's Summarize The minilesson targeted in the fascinating concept of the cube of a binomial The math journey around the cube of binomial starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young mindsNCERT Solutions Class 9 Maths Chapter 2 – Polynomials Exercise 25 are given here These NCERT Maths solutions are created by our subject experts which makes it easy for students to learn The students use it for reference while solving the exercise problems The fifth exercise in Polynomials Exercise 25 discusses the Algebraic Identities
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X a /x b = x ab = 1/x ba;The formula is (xy)³=x³y³3xy(xy) Proof for this formula step by step =(xy)³ =(xy)(xy)(xy) ={(xy)(xy)}(xy) =(x²xyxyy²)(xy) =(xy)(x²y²2xy find x^3y^3 The coordinates of point Y are giving The midpoint XY is (3,5) Find the coordinates of point X
Polynomial Examples Find the remainder when x 4 x 3 – 2x 2 x 1 is divided by x – 1 Solution Here, p(x) = x 4 x 3 – 2x 2 x Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given (i) Area 25a2 – 35a 12 (ii) Area 35y2 13y – 12 Solution (i) We have, area of rectangle = 25a 2 – 35a12 = 25a 2 – a – 15a12 • (x – y) 3 = x 3 – y 3 – 3xy(x – y) • x 3 y 3 z 3 – 3xyz = (x y z)(x 2 y 2 z 2 – xy – yz – zx) Also, check the NCERT Solutions for Class 9 Maths Chapter 2 from the
1 Explanation We know that algebraic formula, (x y) 3 = x 3 y 3 3xy (x y) put the value of x y in given equation given, x y = 1 1 = x 3 y 3 3xy X 1?2 View Full Answer Here, exponent of every variable is a whole number, but x 10 y 3 t 50 is a polynomial in x, y and t, ie, in three variables So, it is not a polynomial in one variable Ex 21 Class 9 Maths Question 2
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If x y z = 0, show that x3 y3 z3 = 3xyz Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to getX 3 y 3 3xy = 1CBSE NCERT Notes Class 9 Maths Polynomials Show Topics Class 9 Maths Polynomials Algebraic Identities Algebraic Identities Algebraic identity is an algebraic equation that is true for all values of the variables occurring in it ( x y) 2 = x2 2 xy y2 ( x – y) 2 = x2 – 2 xy y2 x2 – y2 = ( x y) ( x – y)
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We know that algebraic formula, (x y) 3 = x 3 y 3 3xy (x y) put the value of x y in given equation given, x y = 1 1 = x 3 y 3 3xy X 1 ⇒ x 3 y 3 3xy = 1 Previous Question Next Question Your comments will be displayed only after You are very important to us For any content/service related issues please contact on this number / Mon to Sat 10 AM to 7 PM Answer (xy)^3 = (xy)^2 (xy) = (x^2y^22xy) (xy) = x^3xy^22x^2yx^2yy^32xy^2 = x^3y^33x^2
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State reasons for your answer Ans (i) 4x 2 – 3x 7 ⇒ 4x2 – 3x 7x° ∵ All the exponents of x are whole numbers ∴ 4x 2 – 3x 7 is a polynomial in one variable (ii) ∵ All the exponents of yXy yz zx is a quadratic polynomial in x, y and z If x y = 12, and xy = 27, then find the value of x3 y3 Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queries
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Login Create Account (xy) 3 = x 3y 3 3xy(xy)(4) 3 =x 3y 3 3(21)464=x3y3252x 3y 3 =x 3y 3 =1 0Get FREE NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 25 We have created Step by Step solutions for Class 9 maths to help you to revise (x y) 3 = x 3 3x 2 y 3xy 2 y 3 = x 3 y 3 3xy(x y) So 9 3 = x 3 y 3 3*10*9 x 3 y 3 = 729 270 = 459 Alan
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Ĺet x^yy^x=(xy)^3=x^3y^33xy(xy) Or,x^yy^x=x^3y^39xy again x=3y so x^3y^39xy=(3y)^3y^39(3y)y=2727y9y^2y^3y^39y^227=5427y Now we got 54 27y=27, or 27y=27,y=1 Then x=31=2 The values of x& y only satisfy xy=3 and doen't satisfy x^yy^x=27 So there is no solution for the values of x & yX y is a binomial in which x and y are two terms In mathematics, the cube of sum of two terms is expressed as the cube of binomial x y It is read as x plus y whole cube It is mainly used in mathematics as a formula for expanding cube of sum of any two terms in their terms ( x y) 3 = x 3 y 3 3 x 2 y 3 x y 21 Which of the following expressions are polynomials in one variable and which are not?
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this formula can be derived from (x y) 3 = x 3 y 3 3xy (x y) x 3 y 3 = (x y) 3 3xy (x y) x 3 y 3 = (x y) (x y) 2 3xy = (x y) x 2 y 2 2xy 3xy = (x y) (x 2 xy y 2 ) Was this answer helpful?We know that (x y) 3 = x 3 y 3 3xy(x y) Using Identity VII ⇒ x 3 y 3 = (x y) 3 3xy(x y) x 3 y 3 = (x y){(x y) 2 3xy} ⇒ x 3 y 3 = (x 5 Linear Polynomial A polynomial of degree one is called a linear polynomial eg, x √7 is a linear polynomial in x, y and z √2 µ 3 is a linear polynomial in µ 6 Quadratic Polynomial A polynomial of degree two is called a quadratic polynomial eg;
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Here given are, XY=7, let's say it is formula 1 in order to make it kinda convenient and easy to understand And XY=10, let's mark it as 2 Now, see formula 1 can be also written as,Telangana SCERT Class 9 Math Chapter 2 Polynomials and Factorisation Exercise 25 Math Problems and Solution Here in this Post Telanagana SCERT Class 9 Math Solution Chapter 2 Polynomials and Factorisation Exercise 25Maths Tutor Chandigarh, Chandigarh, India 486 likes 7 talking about this My self Sujit Adhikari from Chandigarh If you need Mathematics teacher, please feel free to contact me at
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Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeT 3 = 91 3 x y (x y) = 91 3 x y t Now from result 1 we know xy in terms of t Substituting in above, we get cubic in t, t 3 − 75 t 1 = 0 On solving for t, we get 3 solns t=7,, Now we know t = xy, on substituting for t in result 1 ,we get the value of xy As we know now xy and (xy) we can solveXXX=15 is equivalent to 3x=15 If you divide each side of the equation by 3, you get x=5 Then, since you know the value of x, you can combine like terms in xyy=35 xyy=35 would be equivalent to 2yx=35 You can then substitute 5 for x, making the equation 2y5=35 Subtract 5 from each side to get 2y=30
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Quadratic equation, for any given x if ax 2 bx c =0 then x has 2 solutions x=(b√(b 2 4ac)/2a, x=(b√(b 2 4ac)/2a x a y b is not equal to (xy) abPolynomial equation is of four types Monomial This type of polynomial contains only one term For example, x 2 , x, y, 3y, 4z Binomial This type of polynomial contains two terms For example, x 2 – 10x Trinomial This type of polynomial contains three terms For example, x 2 – 10x9 Quadratic Polynomial This type of polynomialX 0 =1 x a y a = (xy) a, 2 2 3 2 = 6 2;
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Using formula, (x – y) 3 = x 3 – y 3 – 3xy(x – y) (99) 3 = (100 – 1) 3 = (100) 3 – 1 3 – (3 × 100 × 1) (100 – 1) = – 1 – 300(100 – 1Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack Exchange If xy = 4 and xy = 21 then find the value of x3 y3 Maths Polynomials NCERT Solutions;
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(xy) 3 = x 3 y 3 3xy(x y) x 2 y 2 = (x y)(x y) x2 = 1/x 2, 24 = 1/16 = 1/2 4 (x a)(x b) = x ab; (ii) (2a – 3b) 3 = (2a) 3 – (3b) 33(2a)(3b)(2a3b) Using identity (xy) 3 =x 3y 33xy(xy) = 8a 327b 318ab(2a3b) = 8a 3 – 27 b 3 – 36a 2 b 54ab 2 =8a 3 – 36a 2 b 54ab 2 – 27 b 3 Question 7 Evaluate the following using suitable identities (i) (99) 3Start your 48hour free trial to unlock this answer and thousands more Enjoy eNotes adfree and cancel anytime
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(x y z) 2 = x 2 y 2 z 2 2xy 2yz 2zx (x y) 3 = x 3 y 3 3xy(x y) (x – y) 3 = x 3 – y 3 – 3xy(x – y) x 3 y 3 z 3 – 3xyz = (x y z)(x 2 y 2 z 2 – xy – yz – zx;Now your easily get the answer X×3 Y×3 = 9×3 5×3 this implies, 27–15=12 Hence 12 is the right answer for this I would suggest a trick for that make a pair in which XY =4 and choose that no if we multiply both then they give less than 45 After 2–3 attempt if you are beginners you can easily find the correct pair for all equationsAnswer(xy)³=x³y³3xy(xy) (xy)³= (xy)(xy)(xy) (xy)²(xy) = (x²y²2xy) (xy) = x(x²y²2xy) y(x²y²2xy) = x³xy²2x²yx²yy³2xy²
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Near (x, y)=(3245, 197), (309, 845), (25, 9) and (2365, 15) And since the two equations can be combined into a quartic in x, (or a quartic in y) and a quartic has 4 roots in the complex numbers and we have found 4 real roots then these are the only solutions even if you allowed x and y to be complex numbers = x^3 3x^2y 3xy^2 y^3 = x^3 y^3 3xy(x y) Also, Read Cube of a Binomial Cube of Sum of Two Binomials Examples 1 Determine the expansion of (x 2y)^3 Solution The given expression is (x 2y)^3 We have an equation on cubes like (x y)^3 = x^3 y^3 3xy(x y) By comparing the above expression with the (x y)^3 Here, xTutor Contact tutor 7 months ago Use identity ( a b)^3 = a^3 b^3 3ab (a b ) Put a= x and b= y ( x y)^3 = x^3 y^3 3xy ( x y ) In further step 3xy can be multiplied inside the bracket The answer is 👍 Helpful
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Xy=7 (xy)³=7³ =343 (xy)³=(xy)(x²2xyy²) =x³2x²yxy²x²y2xy²y³ =x³y³3xy(xy) x³y³=3433xy(xy) =3433(7) =364Solution (By Examveda Team) Given, xy = 2 cubing both sides (xy) 3 = 2 3 => x 3 y 3 3xy ( xy) = 8 => x 3 y 3 3×15×2= 8 => x 3 y 3 90 = 8 => x 3 y 3 = 0 Identity (x – y) 3 = x 3 – y 3 – 3xy(x – y) (1000 – 2) 3 = 1000 3 – 2 3 – 3*1000*2(1000 – 2) = – 8 – 6000(1000 – 2) = – 8 – 100 = Factorise each of the following (i) 8a 3 b 3 12a 2 b 6ab 2 (ii) 8a 3 – b 3 – 12a 2 b 6ab 2 (iii) 27 – 125a 3 – 135a 225a 2
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2y=2 y=1 Hence, putting the value of y again in any of the above three equations will give the value of x So, taking equation x=y5 x=1–5 x=4 So the final answers are x=4 and y=1 For any clarification, please update in comments And if you liked the answer do upvote and sorry for any grammatical mistakes
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