Question

if x+1/3=3 then x^4 + 1/x^4=?​

Answer 1

Step-by-step explanation:

x+1/3=3

3x+1=3

x=2/3

then, (2/3)^4+(2/3)^-4 =0

Answer 2

SOLUTION

We have,

$x + \frac{1}{x} = 3$

Squaring both sides, we get

$( {x}^+ \frac{1}{x} ) {}^{2} = {3}^{2} \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 9 \\ \\ = > {x}^{2} + \frac{1}{x {}^{2} } + 2 = 9 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2 = {x}^{2} + \frac{1}{ {x}^{2} } = 7$

Now,

${x}^{2} + \frac{1}{ { {x}^{2}} } = 7 \\ \\ = > ( {x}^{2} + \frac{1}{ {x}^{2} }) {}^{2} = {7}^{2} \\ \\ = > ({x}^{2} ) {}^{2} + ( \frac{1}{ {x}^{2} } ) {}^{2} + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 49 \\ \\ = > {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 49 \\ \\ = > {x}^{4} + \frac{1}{ {x}^{4} } = 49 - 2 \\ \\ = > {x}^{4} + \frac{1}{ { {x}^{4} }} = 47$

hope it helps ☺️