Question

If 3x + 4y = 16 and xy = 4, find the value of 9x² + 16y².

Answer 1

Given that (3x + 4y) = 16 and xy = 4,

We need to find 9x² + 16y²,

We know that,

(a + b)² = a² + b² + 2ab

Consider the square of 3x + 4y:

∴ (3x + 4y)² = (3x)² + (4y)² + 2 × 3x × 4y

⇒ (3x + 4y)² = 9x² + 16y² + 24xy     ...(1)

Substitute the values of (3x + 4y) and xy,

In the above equation (1), we have,

(3x + 4y)² = 9x² + 16y² + 24xy

⇒ (16)² = 9x² + 16y² + 24(4)

⇒ 256 = 9x² + 16y² + 96

⇒ 9x² + 16y² = 256 − 96

∴ 9x² + 16y² = 160