Question
Download Solution PDFIf \((5y + \frac{5}{y}) = 11\), find the value of \((y^2 + \frac{1}{y^2})\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used
(x + y)2 = x2 + y2 + 2xy
Calculation
According to the question:
Divide the expression by 5.
= y + 1/y = 11/5
Squaring both sides
= y2 + 1/y2 + 2 = 121/25
= y2 + 1/y2 = 121/25 - 2
= y2 + 1/y2 = 71/25
= y2 + 1/y2 = 2(21/25)
The answer is 2(21/25).
Last updated on Jul 10, 2025
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