Math, asked by shauryakaushik, 7 months ago

if x +1/x=2,then find x^4 =1/x^4

Answers

Answered by ironmanavenger0890
0

Answer:

So the given equation is, x+1/x=2.

Thus, 2x=x+1.

Hence, x=1.

I hope we are clear till here.

The question asked is x^4 - 1/x^4.

Putting the value of x that we obtained from the given equation(i.e. x=1) in the second equation we get,

1^4 - 1/1^4 = 1 -1/1 = 1-1 = 0.

Looks like the above solution is for the equation:

[ (x+1)/x] = 2

No problem….I will write the other solution too.

The above equation can also be perceived as

x + (1/x) = 2

So, in this case we multiply LHS and RHS with X.

We get,

x^2 + 1 = 2x

~ x^2 - 2x + 1 = 0

Applying the quadratic Formula,

i.e. x = [{ -b + √D}/2a] or x = [{ -b - √D}/2a]

where, D =√(b^2 - 4ac).

So we have, a=1; b=-2; c=1 and D=0.

Thus, putting in the quadratic equation we get,

x = [{2 + 0}/2]

Thus, x = 1.

Also, x=1 satisfies the equation. Thus, x=1 is the solution for the given equation.

hence the answer to x^4+1/x^4 = 0

Did I make it complicated?

if you find it to be useful please mark it the brainliest

HOPE THIS HELPS

Thank you!

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