SOLUTION: The sum of a number and its reciprocal is 5/2. What is the number and reciprocal?

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Question 102444: The sum of a number and its reciprocal is 5/2. What is the number and reciprocal?
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be "x
EQUATION:
x + 1/x =5/2
Multiply thru by 2x to get:
2x^2+2 = 5x
2x^2-5x+2 = 0
2x^2-4x-x+2=0
2x(x-2)-(x-2)=0
(x-2)(2x-1)=0
x = 2 or x = 1/2
=============
Cheers,
Stan H.

Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
X%2B1%2FX=5%2F2
X%5E2%2B1=%285%2F2%29%2AXMultiply both sides by X.
X%5E2-%285%2F2%29%2AX%2B1=cross%28%285%2F2%29%2AX%29-cross%28%285%2F2%29%2AX%29Additive inverse of %285%2F2%29%2AX
X%5E2-%285%2F2%29%2AX%2B1=0Quadratic equation.
We can solve this equation using the quadratic formula where the solution for
aX%5E2%2Bb%2AX%2Bc=0 is solved by
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this case a=1,b=-5%2F2,c=1
x+=+%28-%28-5%2F2%29+%2B-+sqrt%28+%285%29%5E2%2F%282%29%5E2-4%2A1%2A1%29%29%2F%282%2A1%29+Substitute into the quadratic formula.
2x+=+%285%2F2+%2B-+sqrt%28+25%2F4-4%29%29%29+Multiply both sides by 2, just for convenience.
2x+=+%285%2F2+%2B-+sqrt%28+25%2F4-16%2F4%29%29%29+Subtract fractions in the square root, need same denominator.
2x+=+%285%2F2+%2B-+sqrt%28+9%2F4%29%29%29+Simplify.
2x+=+%285%2F2+%2B-++3%2F2%29+
Two solutions are
1.2x+=+%285%2F2+%2B++3%2F2%29+
1.2x=8%2F2
1.x=2
and
2.2x+=+%285%2F2+-+3%2F2%29+
2.2x+=+%282%2F2%29+
2.x+=+1%2F2%29+
Check your answers
X+%2B+1%2FX+=+5%2F2
2+%2B+1%2F2+=+5%2F2
5%2F2+=+5%2F2
True, good answer.
X+%2B+1%2FX+=+5%2F2
1%2F2+%2B+1%2F%281%2F2%29+=+5%2F2
1%2F2+%2B+2+=+5%2F2
5%2F2+=+5%2F2
True, good answer.