Tick (✓) the correct answer:

Question:

Tick (✓) the correct answer:

If $\left(x-\frac{1}{x}\right)=6$, then $\left(x^{2}+\frac{1}{x^{2}}\right)=?$

(a) 36

(b) 38

(c) 32

(d) $36 \frac{1}{36}$

 

Solution:

(b) 38

$\left(x-\frac{1}{x}\right)=6$

$\Rightarrow$ Squaring both the sides:

$\Rightarrow\left(x-\frac{1}{x}\right)^{2}=(6)^{2}$

$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}-2(x)\left(\frac{1}{x}\right)\right)=36$

$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}\right)-2=36$

$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}\right)=36+2$

$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}\right)=38$

 

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