Question

If x- y = 9 and xy = 16, find the value of x square + y square

Answer 1

113, is the answer. Hope you got

Answer 2

Given,

x - y = 9,

xy = 16.

To find,

x² + y².

Solution,

From the given values of (x - y) and (xy), we can find the value of x² + y², by using the algebraic identity

(x - y)² = x² - 2xy + y²     ...(1)

Rearranging the equation (1), we can see that, the required value,

x² + y² = (x - y)² + 2xy     ...(2)

Substituting the values,

x - y = 9, and,

xy = 16 in the above equation (2), we get

x² + y² = (9)² + 2·(16)

⇒ x² + y² = 81 + 32

⇒ x² + y² = 113

Therefore, when x - y = 9, and xy = 16, the value of x² + y² will be 113.