Question

If(x+1/x) =3 find the value of (x4+1/x4)

Answer 1

I hope it will be answer of your question

Answer 2

Answer:

47 is your answer. Thx.

Step-by-step explanation:

$x + \frac{1}{x } = 3 \: \: \: \: ...(given)$

Squaring on both sides,

$( {x + \frac{1}{x} })^{2} = {3}^{2}$

Now, expand this by algebraic identity,

(a+b)² = a²+2ab+b²

Therefore,

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

${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9$

${x}^{2} + \frac{1}{ {x}^{2} } = 7$

Squaring on both sides,

${(x^{2} + \frac{1}{ {x}^{2} } )}^{2} = 49$

${x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 49$

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

$\huge \bold \pink{ {x}^{4} + \frac{1}{ {x}^{4} } = 47}$