Question

If x + 1/x = 6 then find the value of x^4 + (1/x)^4

Answer 1

x+1/x=6
Xsq. + 1/xsq. +2*x*1/x. = 6square
Xsq +1/xsq. = 36-2
Xsq + 1/xsq =34
again squaring both side...
x power 4 + 1/x power 4 = 34sq. -2
have ur answer is
1156-2=1154.......

Answer 2

Answer:

$x^4+\frac{1}{x^4}=1154$

Step-by-step explanation:

It is given that $x+{\frac{1}{x}}=6$, then squaring on both the sdies, and using the identity $(a+b)^2=a^2+b^2+2ab$, we get

⇒$(x+\frac{1}{x})^2=(6)^2$

⇒$x^2+\frac{1}{x^2}+2=36$

⇒$x^2+\frac{1}{x^2}=34$

Now, again squaring on both the sides, we get

$(x^2+\frac{1}{x^2})^2=(34)^2$

⇒$x^4+\frac{1}{x^4}+2=1156$

⇒$x^4+\frac{1}{x^4}=1154$

which is the required value.