If \((5y + \frac{5}{y}) = 11\), find the value of \((y^2 + \frac{1}{y^2})\).

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SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 2)
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  1. \(2\frac{21}{25}\)
  2. \(1\frac{21}{25}\)
  3. \(3\frac{21}{25}\)
  4. \(4\frac{21}{25}\)

Answer (Detailed Solution Below)

Option 1 : \(2\frac{21}{25}\)
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Detailed Solution

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Formula 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).

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