Question 78786: square root of x+40-(minus)sqrare root of x =4
square root of y+10-(minus) square root of y-2 =2
thanks! Answer by mathdoc314(58) (Show Source):
You can put this solution on YOUR website! This is two problems. Please ask the second problem separately or work it yourself after you see the technique.
To solve algebraically, it's necessary to get rid of the square roots in the expression. I tried to do this with tricks like: rewrite it with
but this did not seem to simplify very well. So I tried this instead and it worked.
Let a = and b =
(I did this so a will be smaller than b)
Then solve for a and b like this
a^2 = x
b^2 = x + 40
therefore b^2 = a^2 + 40.
The problem stated
which now is: b - a = 4.
b^2 = a^2 + 40
b - a = 4
Substitute in for a:
a = b - 4
b^2 = (b-4)^2 + 40
b^2 = (b^2 - 8 b + 16) + 40
The b^2 cancels out on both sides
0 = -8 b + 56
8b = 56
b = 7
a = b-4 = 7-4 = 3
Don't forget to find x
Evaluate it twice to show it's right: --> --> -->
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