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Real Root Product (Posted on 2016-04-09) Difficulty: 3 of 5
Determine the product of real roots of this equation:
x2 + 18x + 30 = 2√( x2 + 18x + 45)

No Solution Yet Submitted by K Sengupta    
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Solution Solution Comment 1 of 1
Let y = x^2 + 18x.  Then the equation becomes y + 30 = 2*sqrt[y+45].
This simplifies to the quadratic y^2 + 56y + 720 = 0, which has roots -20 and -36.

Checking these roots: y=-20 yields 10=10 but y=-36 yields -6=+6.  So only the roots corresponding to y=-20 are solutions.

Then y=-20 implies x^2 + 18x = -20, or x^2 + 18x + 20 = 0, which implies the product of the roots of the equation is 20, which is the answer being sought.

  Posted by Brian Smith on 2016-04-09 11:25:23
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