Question

x+1/x=10, find the value of x^2+1/x^2​

Answer 1

$x + \frac{1}{x} = 10$

Squaring Both Sides

$(x + \frac{1}{x} ) {}^{2} = {10}^{2}$

Evaluate LHS term In Form (a+b)²=a²+b²+2ab

$( {x}^{2} + \frac{1}{x {}^{2} } + 2 \times \cancel{x} \times \frac{1}{ \cancel{x}} ) = 100 \\ \\ ( {x}^{2} + \frac{1}{x {}^{2} } + 2) = 100 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 100 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 98$

$\huge{\boxed{ {x}^{2} + \frac{1}{ {x}^{2} } = 98} }$