SOLUTION: Find Positive Root: {{{ 2x^-1+ (x-1)^-1=4 }}}

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Question 41306: Find Positive Root: +2x%5E-1%2B+%28x-1%29%5E-1=4+
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the positive root:
2x%5E-1+%2B+%28x-1%29%5E-1+=+4 Simplify.
2%2Fx+%2B+1%2F%28x-1%29+=+4 Add the fractions on the left side.
%282%28x-1%29+%2B+x%29%2F%28x%28x-1%29%29+=+4 Simplify.
%283x-2%29%2F%28x%5E2-x%29+=+4 Multiply both sides by x^2-x
3x-2+=+4%28x%5E2-x%29 Simplify.
3x-2+=+4x%5E2-4x Subtract 3x-2 from both sides.
4x%5E2-7x%2B2+=+0} Solve the quadratic equation by the quadratic formula:x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x+=+%28-%28-7%29%2B-sqrt%28%28-7%29%5E2-4%284%29%282%29%29%29%2F2%284%29 Simplify.
x+=+%287%2B-sqrt%2849-32%29%29%2F8
x+=+%287%2B-sqrt%2817%29%29%2F8
One positive root is:
x+=+%287%2F8%29%2B%28sqrt%2817%29%29%2F8 = 1.40 (approximately)
The other positive root is:
x+=+%287%2F8%29-%28sqrt%2817%29%29%2F8 = 0.36 (approximately)