Question

if x +1/x =6 find x⁶ +1/x⁶ ​

Answer 1

Answer:

39,202

Step-by-step explanation:

x+1/x =6

(x+1/x)³=6³

x³+1/x³+3(x+1/x)=216

x³+1/x³+3(6)=216

x³+1/x³=216-18

x³+1/x³=198

(x³)²+(1/x³)²+2=198²

x6+1/x6=39,204-2

x6+1/x6=39,202

Answer 2

Given given data in the question are,

$\frac{x+1}{x} =6$

We have to find the value of $\frac{x^{6} +1}{x^{6} }$ so,

For finding the value of $x$.

multiplying $x$ by $6$ ,we get

$x+1=6x$

$1=6x-x\\1=5x\\x=\frac{1}{5}$

∴ $x=$$\frac{1}{5}$

the value of x is $\frac{1}{5}$. so , putting the values of x in $\frac{x^{6} +1}{x^{6} }$, we get

$=\frac{x^{6} +1}{x^{6} } \\=\frac{\frac{1}{5} ^{6} +1}{\frac{1}{5} ^{6} }$

By separating the addition terms, we get

$=1+\frac{1}{\frac{1^{6} }{5^{6} } }$

by shifting the $15625$ to numerator,we get

$=1 +15625$

$=15626$

Therefore, the value of $\frac{x^{6}+1 }{x^{6} } =15626$