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

Solving, ⇒ (3x + 4y) 2 = (3x) 2 + (4y) 2 + 2 × 3x × 4y ⇒ (3x + 4y) 2 = 9x 2 + 16y 2 + 24xy Substituting values we get : ⇒ 16 2 = 9x 2 + 16y 2 + 24 × 4 ⇒ 256 = 9x 2 + 16y 2 + 96 ⇒ 9x 2 + 16y 2 = 256 - 96 = 160. Hence, 9x 2 + 16y 2 = 160.

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Mathematics

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

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Answer

Solving,

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

⇒ (3x + 4y)² = 9x² + 16y² + 24xy

Substituting values we get :

⇒ 16² = 9x² + 16y² + 24 × 4

⇒ 256 = 9x² + 16y² + 96

⇒ 9x² + 16y² = 256 - 96 = 160.

Hence, 9x² + 16y² = 160.

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

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