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Question

If 3x+5y=11 and xy=2, find the value of 9x2+25y2.

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Solution

Given: 3x+5y=11, xy=2

To find 9x2+25y2

3x+5y=11
Squaring both sides, we get
(3x+5y)2=(11)2

9x2+25y2+30xy=121

9x2+25y2+30×2=121 (xy=2)

9x2+25y2+60=121
9x2+25y2=12160

9x2+25y2=61

9x2+25y2=61.


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