Question

If x² + y² = 34 and xy = `10 1/2`, find the value of 2(x + y)² + (x − y)².

Answer 1

Here, x² + y² = 34 and xy = `10 1/2=21/2`

Using the identity:

(x + y)² = x² + y² + 2xy

(x − y)² = x² + y² − 2xy

Solving each expression,

(x + y)² = 34 + 2 `(21/2)`

(x + y)² = 34 + 21

∴ (x + y)² = 55

(x − y)² = 34 − 2 `(21/2)`

(x − y)² = 34 − 21

∴ (x − y)² = 13

Let’s put in the values in the final expression.

2(x + y)² + (x − y)²

= 2(55) + 13

= 110 + 13

= 123

Hence, 2(x + y)² + (x − y)² = 123