Question

If x^2 plus y^2=4 and x-y=3
then find the value of x^3-y^3​

Answer 1

Answer :-

Value of x³ - y³ is 9/2.

Explanation :-

Finding the value of xy

We know that

(x - y)² = x² + y² - 2xy

Here

• x - y = 3

• x² + y² = 4

By substituting the values in the identity

⇒ (3)² = 4 - 2xy

⇒ 9 = 4 - 2xy

⇒ 2xy = 4 - 9

⇒ 2xy = - 5

⇒ xy = - 5/2

Finding the value of x³ - y³

We know that

x³ - y³ = (x - y)(x² + y² + xy)

Here

• x - y = 3

• x² + y² = 4

• xy = - 5/2

By substituting the values in the identity

⇒ x³ - y³ = 3{4 + (-5/2)}

⇒ x³ - y³ = 3(4 - 5/2)

⇒ x³ - y³ = 3{(8 - 5)/2}

⇒ x³ - y³ = 3(3/2)

⇒ x³ - y³ = 9/2

∴ the value of x³ - y³ is 9/2.