If 3x - 4y = 16 and xy = 4, find the value of 9x 2 + 16y 2 .

We know that, a 2 + b 2 = (a - b) 2 + 2ab. 9x 2 + 16y 2 = (3x) 2 + (4y) 2 = (3x - 4y) 2 + 24xy. Substituting values we get, ⇒ 9x 2 + 16y 2 = (16) 2 + 24 × 4 ⇒ 9x 2 + 16y 2 = 256 + 96 ⇒ 9x 2 + 16y 2 = 352. Hence, 9x 2 + 16y 2 = 352.

Mathematics

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

Expansions

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Answer

We know that,

a² + b² = (a - b)² + 2ab.

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

Substituting values we get,

⇒ 9x² + 16y² = (16)² + 24 × 4

⇒ 9x² + 16y² = 256 + 96

⇒ 9x² + 16y² = 352.

Hence, 9x² + 16y² = 352.

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Mathematics

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

Expansions

Answer

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Mathematics

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

Expansions

Answer

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