Question

If x = 3 + √8, find the value of (x² + 1/x²)​

Answer 1

Answer:

34

Step-by-step explanation:

given x= 3+√8

squaring on both sides

(x)^2=(3+√8)^2

x^2=(3)^2+2(3)(√8)+(√8)^2

x^2=9+6√8+8

x^2=17+6√8

1/x^2=17-6√8

x^2+1/x^2=17+6√8+17-6√8

=17+17

=34

{x^2 means x power 2}

Answer 2

x = 3 + √8

______ [GIVEN]

• We have to find the value of x² + $\dfrac{1}{ {x}^{2} }$

______________________________

• x = 3 + √8

• $\dfrac{1}{x}$ = $\dfrac{1}{3 + \sqrt{ 8}}$

=> $\dfrac{1}{3 + \sqrt{ 8}} \: \times \: \dfrac{3 \: - \: \sqrt{8} }{3 \: - \: \sqrt{8} }$

=> $\dfrac{3 \: - \: \sqrt{8} }{9 \: - \:8 }$

=> 3 - √8

______________________________

(x + $\dfrac{1}{x})$ = 3 + √8 + 3 - √8

=> 6

• Do squaring on both sides

=> $( {x \: + \: \dfrac{1}{x}) }^{2}$ = (6)²

=> x² + $\dfrac{1}{ {x}^{2} }$ + 2 $(\dfrac{x}{x})$ = 36

=> x² + $\dfrac{1}{ {x}^{2} }$ + 2 = 36

=> x² + $\dfrac{1}{ {x}^{2} }$ = 36 - 2

____________________________

x² + $\dfrac{1}{ {x}^{2} }$ = 34

____________ [ANSWER]