Question

if x+1/x=6, find x^2+1/x^2​

Answer 1

Step-by-step explanation:

(x+1/x)². = (6)²

x²+1/x²+2x*1/x². =36. (x. * 1/x will cancel then we get 1 then we multiple 1 to 2 we get 2)

x²+1/x² +2=36

x²+1/x²=36-2

x²+1/x². =34

Answer 2

Step-by-step explanation:

$\blue{\it{\underline{question} : - }}$

$x + \frac{1}{x} = 6$

$\green{\bold{\underline{solution : - }}}$

${\mathbb{\boxed{squaring \: both \: sides \: we \: found}}}$

${\bold{\implies{ {x}^{2} + {( \frac{ 1}{x}) }^{2} = {6}^{2}}}}$

we know,

$\boxed{ {a}^{2} + {b}^{2} + 2ab}$

Now,

$\implies{\bold{ {x}^{2} + {( \frac{1}{x} )}^{2} + 2 \times x \times \frac{1}{x}}} = 36$

$\implies {x}^{2} + { (\frac{1}{x}) }^{2} = 36 - 2$

$\implies{ {x}^{2} + { (\frac{1}{x}) }^{2} = 34}$