Question

Please solve this problem

Answer 1

Answer:

this answe is your questions

I hope u will understand this answer

Answer 2

Answer :

To Find :

$x^{4}\: + \: \dfrac{1}{x^{4}} \: = \: ?$

Given :

$x \: + \: \dfrac{1}{x} \: = \: 3$

Solution :

$x \: + \: \dfrac{1}{x} \: = \: 3$

square both sides

${\Big(x \: + \: \dfrac{1}{x}\Big)}^2 \: = \: (3)^{2}$

$x^{2} \:+ \:\dfrac{1}{x^{2}} \:+\: x\times \dfrac{1}{x} \times 2 \: = \: 9$

$x^{2} \:+\: \dfrac{1}{x^{2}}\: + \:2 \: = \: 9$

$x^{2} \:+\: \dfrac{1}{x^{2}} \: = \: 9\: - \: 2$

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

Square it again to achieve the required value :

$\Big(x^{2} \:+\: \dfrac{1}{x^{2}}\Big)^{2} \: = \: 49$

$x^{4} \: + \: \dfrac{1}{x^{4}} \: + \: 2 \: = \: 49$

$x^{4} \: + \: \dfrac{1}{x^{4}} \: = \: 49 \: - \: 2$

$x^{4} \: + \: \dfrac{1}{x^{4}} \: = \: 47$

As per solution the respective value is 47

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