If 3x + 5y = 14 and xy = 6, then what is the value of 9x2 + 25y2 ?
If 3x + 5y = 14 and xy = 6, then what is the value of 9x2 + 25y2 ? Correct Answer 16
Given:
3x + 5y = 14 and xy = 6
Formula used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
(3x + 5y)2 = (14)2
⇒ 9x2 + 25y2 + 2 × 3x × 5y = 196
⇒ 9x2 + 25y2 + 30xy = 196
⇒ 9x2 + 25y2 = 196 - 30 × 6
⇒ 9x2 + 25y2 = 16
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Feb 20, 2025