যদি \(y + {{1} \over y} = 3\) হয়, তাহলে \({{1} \over y^3} + y^3 + 2 \) এর মান কত?

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Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 3)

Answer 1

প্রদত্ত:

\(y + {{1} \over y} = 3\)

অনুসৃত ধারণা:

(a + b)³ = a³ + b³ + 3ab(a + b)

গণনা:

\(y + {{1} \over y} = 3\)

⇒ \((y + {{1} \over y})^3 = 27\)

⇒ \(y^3 + {{1} \over y}^3 +3(y +\frac{1}{y})= 27\)

⇒ \(y^3 + {{1} \over y}^3 +3 \times 3= 27\)

⇒ \(y^3 + {{1} \over y}^3 +9= 27\)

⇒ \(y^3 + {{1} \over y}^3= 18\)

⇒ \({{1} \over y^3} + y^3 + 2 \) = 20

∴ নির্ণেয় উত্তর 20

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