#SSC CGL

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Question : If $x^4+\frac{1}{x^4}=194$ and $x^3+\frac{1}{x^3}=?$
Option 1: 52
Option 2: 58
Option 3: 76
Option 4: 67

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Team Careers360 24th Jan, 2024

Answer (1)

Team Careers360 25th Jan, 2024

Correct Answer: 52

Solution : $x^4+\frac{1}{x^4}=194$
Adding 2 on both sides,
⇒ $x^4+\frac{1}{x^4}+2=194+2$
⇒ $(x^2+\frac{1}{x^2})^2=196$
Taking square root on both sides,
⇒ $x^2+\frac{1}{x^2}=14$
Adding 2 on both sides,
⇒ $x^2+\frac{1}{x^2}+2=14+2$
⇒ $(x+\frac{1}{x})^2=16$
Taking square root on both sides,
⇒ $x+\frac{1}{x}=4$
⇒ $(x+\frac{1}{x})^3=4^3$
⇒ $x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=64$
⇒ $x^3+\frac{1}{x^3}+3×4=64$
⇒ $x^3+\frac{1}{x^3}=64-12 = 52$
Hence, the correct answer is 52.

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