Question : If $x+\frac{1}{x}=2$, then $x^3+\frac{1}{x^3}=?$
Option 1: 1
Option 2: 8
Option 3: 2
Option 4: 0
Answer (1)
27th Jan, 2024
Correct Answer: 2
Solution :
$x+\frac{1}{x}=2$
Cubing both sides, we get,
$(x+\frac{1}{x})^3=2^3$
⇒ $x^3 + \frac{1}{x^3}+3\times x\times\frac{1}{x}(x+\frac{1}{x})=8$
⇒ $x^3 + \frac{1}{x^3} + 3(x+\frac1x)=8$
⇒ $x^3 + \frac{1}{x^3} +3\times 2=8$
⇒ $x^3+\frac{1}{x^3}=8-6$
$\therefore x^3+\frac{1}{x^3}=2$
Hence, the correct answer is 2.
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