Question

if x = 5-2√6, find the value of x²+1/x²​

Answer 1

Step-by-step explanation:

${(5 - 2 \sqrt{6}) }^{2} + \frac{1}{ {(5 - 2 \sqrt{6)} }^{2} }$

take LCM !!!

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

then solve it!!

Answer 2

Given :-

$\bullet \: \: \sf{x = 5 - 2 \sqrt{6} }$

To find :-

• x²+1/x²

According to the question,

$\implies\sf{ \dfrac{1}{x} = \dfrac{1}{5 - 2 \sqrt{6} } \times \dfrac{5 + 2 \sqrt{6} }{5 + 2 \sqrt{6} } }$

$\implies \sf{ \frac{1}{x} = \frac{5 + 2 \sqrt{6} }{25 - 24} = 5 + 2 \sqrt{6 } \:\green\bigstar}$

$\implies\sf{ x + \dfrac{1}{ x} = 5 - 2 \sqrt{6} + 5 + 2 \sqrt{6} }$

$\implies \sf{x + \frac{1}{x} = 10 \: \pink\bigstar }$

Squaring on both the sides :

$\implies \sf{ {x}^{2} + \dfrac{1}{ {x}^{2} } = {10}^{2} } \\ \\ \implies \sf{ {x}^{2} + \frac{1}{ {x}^{2}} + 2 \times x \times \frac{1}{ x} = 100} \\ \\ \implies \sf{{x}^{2} + \frac{1}{ {x}^{2} } + 2= 100 } \\ \\ \implies \sf{ {x}^{2} + \frac{1}{ {x}^{2} } = 100 - 2 } \\ \\ { \underline{ \boxed{\implies {\sf{ {x}^{2} + \frac{1}{ {x}^{2} } = 98}}}}} \orange\bigstar$