Question

if x-1/x=2, find x^4+1/x^4​

Answer 1

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 Shridhar Acharya Formula,

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

where, ‘a' and ‘b’ are the coefficients of ‘x^2’ and ‘x’ respectively. ‘c’ is the constant. And, D =√(b^2 - 4ac).

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

Thus, putting in the Shridhar Acharya 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.

The solution can also be found out by breaking the perfect square equation. But here I have the most efficient, effective and general method of solving.

Did I make it complicated?

Thank you!