Question

If
x+1/x =4
Then
x^4+1/x^4=?
​

Answer 1

Answer:

hey here is your answer : it's X

Answer 2

Answer:

Step-by-step explanation:

ysticdMaths AryaBhatta

Hi ,

It is given that ,

x + 1/x = 4 ---( 1 )

Do the square of equation ( 1 ),

( x + 1/x )² = 4²

x² + 1/x² + 2 = 16

x² + 1/x² = 16 - 2

x² + 1/x² = 14 --( 2 )

Again do the square of equation ( 2 ),

( x² + 1/x² )² = 14²

x⁴ + 1/x⁴ + 2 = 196

x⁴ + 1/x⁴ = 196 - 2

= 194

_______ii method __________

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 .

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