Question

If xy = -30 and x2 + y2 = 61, then find the value of (x + y).

Answer 1

Correct Question :-

If xy = -30 and x² + y² = 61, then find the value of x + y.

Answer :-

x + y = 1

Solution :-

We know that

(x + y)² = x² + y² + 2xy

Here

• xy = - 30

• x² + y² = 61

By substituting the values

⇒ (x + y)² = 61 + 2(-30)

⇒ (x + y)² = 61 - 60

⇒ (x + y)² = 1

⇒ x + y = √1

⇒ x + y = 1

Therefore the value of x + y is 1.

Verification :-

(x + y)² = x² + y² + 2xy

⇒ (1)² = 61 + 2(-30)

⇒ 1 = 61 - 60

⇒ 1 = 1

Identity used :-

• (x + y)² = x² + y² + 2xy