Question

If x − y = 4 and xy = 2 then find the value of x³-y³

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Answer 1

Answer:

Step-by-step explanation:

x-y=4 and xy=2

a/p

(x-y)^2=x^2+y^2-2xy

4^2=x^2+y^2-2*2

which implies x^2+y^2=16-4=12

x^3-y^3=(x-y)(x^2+y^2+xy)

=4(12+2)

=56

Answer 2

Concept:

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Identity I: (a + b)² = a² + 2ab + b²

Identity II: (a – b)2 = a² – 2ab + b²

Identity III: a² – b²= (a + b)(a – b)

Identity IV: (x + a)(x + b) = x² + (a + b) x + ab

Identity V: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Identity VI: (a + b)³ = a³ + b³ + 3ab (a + b)

Identity VII: (a – b)³ = a³ – b³ – 3ab (a – b)

Identity VIII: a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

Given:

If x − y = 4 and xy = 2

Find:

find the value of x³-y³

Solution:

x-y=4 and xy=2

As per question,

(x-y)²=x²+y²-2xy

4²=x²+y²-2*2

which implies x²+y²=16-4=12

x³-y³=(x-y)(x²+y²+xy)

=4(12+2)

=56

Therefore,the value of x³-y³is 56

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