If x^4+1 x^4 =623, than x+1 x = - Vidyadip

MCQ

If $\text{x}^4+\frac{1}{\text{x}^4}=623,$ than $\text{x}+\frac{1}{\text{x}}=$

A
$27$
B
$3\sqrt{3}$
C
$25$
D
$-3\sqrt{3}$

✓

Answer

$3\sqrt{3}$
Solution:
$\Big(\text{x}^4+\frac{1}{\text{x}^4}\Big)=623$
$\Rightarrow(\text{x}^2)^2+\Big(\frac{1}{\text{x}^2}\Big)+2\times\text{x}^2\times\frac{1}{\text{x}^2}=623+2\times\text{x}^2\times\frac{1}{\text{x}^2}$
$\Rightarrow\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)^2=625$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}=\sqrt{625}=25$
Now,
$\Rightarrow(\text{x}^2)+\Big(\frac{1}{\text{x}^2}\Big)+2\times\text{x}\times\frac{1}{\text{x}}=25+2\times\text{x}\times\frac{1}{\text{x}}$
$\Rightarrow\Big(\text{x}+\frac{1}{\text{x}}\Big)^2=27$
$\Rightarrow\text{x}+\frac{1}{\text{x}}=\sqrt{27}=3\sqrt{3}$

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