Answer to Question #158839 in Algebra for Surendra Singh

Question

x+1/x=5, then find the value of x^16+1/x^16 ?

Answer 1

We have given with

$x+1/x=5$

So, $(x+1/x)^2=(5)^2$

Expanding the bracket by using formula

$(a+b)^2=a^2+2ab+b^2$

We get ,

$x^2+2(x)(1/x)+(1/x^2)=25$

Simplifying we have,

$x^2+1/x^2=23$

Taking square on both sides we get

$(x^2+1/x^2)^2=(23 )^2$

$=x^4+2(x^4)(1/x^4)+(1/x^4)=529$ ,

$x^4+1/x^4=529-2$

$=x^4+1/x^4=527$

Again Taking square on both sides we get

$(x^4+1/x^4)^2=(527)^2$

$=x^8+2(x^8)(1/x^8)+1/x^8=277729$ ,

$x^8+1/x^8=277729-2$

$=x^8+1/x^8=277727$

Again ,Taking square on both sides,we have

$x^{16}+1/x^{16}=(277727)^2-2$ So,
Answer:

$(277727)^2-2$