Question

Please answer my question please please please
If X+ one upon x=√7 find value of x^2+1/x^2 and x^4+1/x^4

Answer 1

x + $\dfrac{1}{x}$ = √7

__________ [GIVEN]

x² + $\dfrac{1}{ {x}^{2} }$

and

x⁴ + $\dfrac{1}{ {x}^{4} }$

__________ [TO FIND]

=> x + $\dfrac{1}{x}$ = √7

• Squaring on both sides.

=> $( {x \: + \: \dfrac{1}{x}) }^{2}$ = (√7)²

=> x² + $\dfrac{1}{ {x}^{2} }$ + 2 $(\dfrac{x}{x})$ = 7

=> x² + $\dfrac{1}{ {x}^{2} }$ + 2 = 7

=> x² + $\dfrac{1}{ {x}^{2} }$ = 7 - 2

______________________________

x² + $\dfrac{1}{ {x}^{2} }$ = 5

____________ [ANSWER]

=> x² + $\dfrac{1}{ {x}^{2} }$ = 5

• Squaring on both sides.

=> $( { {x}^{2} \: + \: \dfrac{1}{ {x}^{2} } ) }^{2}$ = (5)²

=> x⁴ + $\dfrac{1}{ {x}^{4} }$ + 2$(\dfrac{ {x}^{2} }{ {x}^{2} })$ (x² + $\dfrac{1}{ {x}^{2} })$ = 25

=> x⁴ + $\dfrac{1}{ {x}^{4} }$ + 2(5) = 25

=> x⁴ + $\dfrac{1}{ {x}^{4} }$ = 25 - 10

______________________________

x⁴ + $\dfrac{1}{ {x}^{4} }$ = 15

_______________ [ANSWER]