Question

please tell with full explanation I will make him as brainliest​

Answer 1

Step-by-step explanation:

Suitable identity =( x+1/x)^2=x^2 + 1/x^2+2

Answer 2

$\bold\green{\underline{Given:}}$

If X+1/X=4

$\bold\green{\underline{Find:X^4+\frac{1}{X^4}=?}}$

$\huge\bold\orange{\underline{Solution:}}$

• Here, square on both sides

$=>(x + \frac{1}{x}) {}^{2} = {5}^{2} \\ \\ => {x}^{2} + 2 \times x \times \frac{1}{x} + \frac{1}{ {x}^{2} } = 25 \\ \\ =>{x}^{2} + \frac{1}{ {x}^{2} } = 25 - 2 \\ \\ => {x}^{2} + \frac{1}{ {x}^{2} } = 23$

• Again squaring on both sides

$=>( {x}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = {23}^{2} \\ \\ =>{x}^{4} + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } + \frac{1}{ {x}^{4} } = 529 \\ \\ => {x}^{4} + \frac{1}{ {x}^{4} } = 529 - 2 \\ \\ => {x}^{4} + \frac{1}{ {x}^{4} } = 527$

Hence,

$\bold\purple{\boxed{X^4+\frac{1}{X^4}=527}}$