If x+1/x=2 then the value of x^2014+1/x^2016
x^2 + 1 = 2 x
x^2 -2x + 1 = 0
(x-1)(x-1) = 0
so
x = 1
x^anything = 1
and 1 + 1/1 = 2
Hey, Bob Pursley answered this hours ago.
To find the value of x^2014 + 1/x^2016, we can utilize the equation x + 1/x = 2. Let's proceed step by step:
1. Multiply both sides of the equation x + 1/x = 2 by x. This gives us x^2 + 1 = 2x.
2. Rearrange the equation to form a quadratic equation. Subtract 2x from both sides to get x^2 - 2x + 1 = 0.
3. Using the quadratic formula, we can solve for x. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± √(b^2 - 4ac)) / 2a.
In this case, a = 1, b = -2, and c = 1. Substituting these values into the quadratic formula, we have:
x = (-(-2) ± √((-2)^2 - 4(1)(1))) / (2(1))
= (2 ± √(4 - 4)) / 2
= (2 ± √0) / 2
= (2 ± 0) / 2
Since the discriminant (√(b^2 - 4ac)) is zero, there is only one solution. Therefore, x = 1.
4. Now that we have found the value of x, we can substitute it back into the expression x^2014 + 1/x^2016:
x^2014 + 1/x^2016 = 1^2014 + 1/1^2016
= 1 + 1/1
= 1 + 1
= 2
So, the value of x^2014 + 1/x^2016 is 2.