Question

if x+1%x=4,find x^4+1%x^4

Answer 1

Answer :

Given,

x + 1/x = 4

Now, squaring both sides, we get

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

=> x^2 + 1/x^2 + (2 * x * 1/x) = 16

=> x^2 + 1/x^2 + 2 = 16

=> x^2 + 1/x^2 = 16 - 2

=> x^2 + 1/x^2 = 14

Again, squaring both sides, we get

(x^2 + 1/x^2)^2 = 14^2

=> x^4 + 1/x^4 + (2 * x^2 * 1/x^2) = 196

=> x^4 + 1/x^4 + 2 = 196

=> x^4 + 1/x^4 = 196 - 2

=> x^4 + 1/x^4 = 194

So, x^4 + 1/x^4 = 194

Another method.

Now,

x^4 + 1/x^4

= (x^2 + 1/x^2)^2 - (2 * x^2 * 1/x^2)

= (x^2 + 1/x^2)^2 - 2

= [ (x + 1/x)^2 - (2 * x * 1/x) ]^2 - 2

= (4^2 - 2)^2 - 2

= (16 - 2)^2 - 2

= 14^2 - 2

= 196 - 2

= 194

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