If ( 3y + 3/y ) = 8 , find the value of ( y²+ 1/(y²) ).

If ( 3y + $\frac{3}{y}$ ) = 8 , find the value of ( y²+ $\frac{1}{y^2}$ ).

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 5 $\frac{1}{9}$ .

3y + 3/y = 8
y + 1/y = 8/3

(y + 1/y)² = y² + 1/y² + 2
⇒ (8/3)² = y² + 1/y² + 2
⇒ 64/9 = y² + 1/y² + 2
⇒ y² + 1/y² = 64/9 − 2 = 64/9 − 18/9 = 46/9 = 5 $\frac{1}{9}$

SSC CHSL 2023 PYQ — Question 61