Question

if x^4 + 1/x^4 = 2 , find x + 1/x​

Answer 1

Answer: We will proceed by whats given

x + 1/x = 2

On squaring we get

x^2 + 1/x^2 + 2 = 4

i.e. x^2 + 1/x^2 = 2

Now again squaring the obtained equation

x^4 + 1/x^4 + 2 = 4

x^4 + 1/x^4 = 2 .

Well thats it ! The answer to the question is 2 .

We used the approach of squaring because notice that the term of 2ab would yeild a constant = 2 , because here a and b are reciprocals and hence cancel each other out i.e. a= x and b=1/x

Thanks and regards .