SOLUTION: Solve the following with substitution
{{{ x^2-3x-sqrt(x^2-3x)=2 }}}
My steps so far are
{{{ U =sqrt(x^2-3x) }}}
{{{ U^2 - U = 2 }}}
{{{ U^2-U-2=0 }}}
{{{ (U-2)(U+1) }
Algebra.Com
Question 1094270: Solve the following with substitution
My steps so far are
U= 2, -1
Then I went back using 2, -1 to plug back in
And ended up getting and from both
But -2 cant be it, so that would leave me with the 4 or 2,-2?
I'm not sure how to go about this.
Found 2 solutions by greenestamps, htmentor:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
You used substitution to find U = sqrt(x^2-3x) is equal to either -1 or 2.
won't give you any solutions, because a square root is never negative.
gives you solutions.
The solutions are x=4 and x=-1; checking shows that both solutions work in the original equation.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
You made the incorrect substitution. You found that u = 2, -1,
but you substituted these values for x instead of u in the expression
And we can reject u = -1 as a solution since a square root cannot be negative.
2 = -> x^2 - 3x - 4 = 0 -> (x-4)(x+1) = 0
So the two solutions are x = -1, x = 4
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