Question

ifx^50+1/x^50=2,then what is the value of x^100+1/x^100

Answer 1

x^50 + 1 / x ^50 = 2

Now, squaring both sides,

( x^50 + 1/ x ^50 ) ^2 = 2^2

x ^100 + 1 / x^100 + 2 × x^50 × 1 / x^50 = 4

x^100 + 1/ x^100 = 4 - 2 = 2.

So, value of x^100 + 1/ x^100 is 2.

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!!}}}$

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Here is your answer.
$x {}^{50} + \frac{1}{x {}^{50} } = 2 \\ now \: squaring \: both \: sides \: we \: get \\ x {}^{100} + \frac{1}{x {}^{100} } + 2 = 2 {}^{2} \\ x {}^{100} + \frac{1}{x {}^{100} } = 4 - 2 \\ x {}^{100} + \frac{1}{x {}^{100} } = 2$
$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope\:it\: helps\: you}}}}}}}}}}}}}}}$