If 3x + 4y = 16 and xy = 4; find the value of 9x2 + 16y2.
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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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The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.