Let x - 1 x =3 and x^3+(1)/(x^3)=k , then characteristic of k with base 10 is:

Correct answer: 3 aligned x - 1 x =3 & x+(1)/(x)-2=9 & x+(1)/(x)=11 x^3+(1)/(x^3)+3(x+(1)/(x))=1331 & x^3+(1)/(x^3)=1298 aligned 3 < _ 10 1298 < 4

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JEE Advanced · Mathematics · Basics of Mathematics

Let x - 1 x =3 and x^3+(1)/(x^3)=k , then characteristic of k with...

Let

\sqrt{x}-\frac{1}{\sqrt{x}}=3

and

x^3+\frac{1}{x^3}=k

, then characteristic of

k

with base 10 is:

\begin{aligned} \sqrt{x}-\frac{1}{\sqrt{x}}=3 & \Rightarrow x+\frac{1}{x}-2=9 \\ \Rightarrow \quad & \Rightarrow x+\frac{1}{x}=11 \\ \Rightarrow \quad x^3+\frac{1}{x^3}+3\left(x+\frac{1}{x}\right)=1331 & \Rightarrow \quad x^3+\frac{1}{x^3}=1298\end{aligned}

\Rightarrow \quad 3 < \log _{10} 1298 < 4