Question

Please Answer this with method

Answer 1

$\underline{\textbf{Hey Mate Here Is Your Answer }}$

$\underline{\textbf{Given That..}}$

$\mathbf{ {x}^{50} + \frac{1}{ {x}^{50} } = 2}$ , Now We Need To Find Value Of $\mathbf{ {x}^{100} + \frac{1}{ {x}^{100} } = ? }$

$\underline{\textbf{Solution..}}$

Now According To Question

$\mathbf{ {x}^{50} + \frac{1}{ {x}^{50} } = 2}$

Now Squaring Both Side ( LHS And RHS ) We Have

$\mathbf{ ({{x}^{50} + \frac{1}{ {x}^{50} }})^{2} = {(2)}^{2} }$

Now By Identity

$\mathbf{ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}$

We Have

$\mathbf{ ( { {x}^{50}) }^{2} + { ({ \frac{1}{ {x}^{50} }) } }^{2} + 2 ({x}^{ 50} ) { (\frac{1}{ {x}^{50} }) }^{2} = {(2)}^{2} }$

Now Simplifying This We Have

$\mathbf{ {x}^{100} + \frac{1}{ {x}^{100} } + 2 = 4}$

Now Taking 2 To RHS We Have..

$\mathbf{ {x}^{100} + \frac{1}{ {x}^{100} } = 4 - 2}$

That Is

$\boxed{ \mathbf{ {x}^{100} + \frac{1}{ {x}^{100} } = 2}}$

$\underline{\textbf{Hence The Required Answer Is}}$

$\boxed{\boxed{\bold{2}}}$

$\mathbf{\mathfrak{Thanks..}}$