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