Question 270701: Find all real solutions to each equation:
64. x^2+x+√(x^2+x)-2=0
Would you square all terms to get rid of the sq root over the (x^2+x) first and then solve for x with a 4th power coeffcient? Thanks for your help!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find all real solutions to each equation:
64. x^2+x+√(x^2+x)-2=0
Would you square all terms to get rid of the sq root over the (x^2+x) first and then solve for x with a 4th power coeffcient?
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Let's see:
x^2 + x - 2 = - sqrt(x^2+x)
(x+2)(x-1) = -sqrt(x^2+x)
[(x+2)(x-1)]^2 = x(x+1)
[(x+2)(x-1)]^2-x(x+1) = 0
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I guess you have no choice here but to go ahead and square, simplify,
solve, and check for extraneous solutions.
Cheers,
Stan H.
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