If x > 0 and y > 0, which of the following is equal to 1/(root x + root (x + y))?
(A) 1/y
(B) Root (2x + y)
(C) Root x/Root(x + y)
(D) (Root x - Root (x + y))/y
(E) (Root (x + y) - Root x)/y
OA: E
Roots problem
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- krusta80
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HG10 wrote:If x > 0 and y > 0, which of the following is equal to 1/(root x + root (x + y))?
(A) 1/y
(B) Root (2x + y)
(C) Root x/Root(x + y)
(D) (Root x - Root (x + y))/y
(E) (Root (x + y) - Root x)/y
OA: E
1/[root (x) + root (x + y)] = ?
Let's try to remove the roots from the denominator by multiplying by [root(x) - root(x+y)] / [root(x) - root(x+y)]
Formula becomes [root(x) - root(x+y)] / (x - x - y) = [root(x+y) - root(x)]/y
E
- Troika
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Thanks for the explanation. Please let me know why you multiplied [root x - root ( x + y)] / [root x - root (x + y)] to get rid of the denominator, instead of multiplying the equation by [root x + root ( x + y)] / [root x + root ( x + y)]? Shouldn't the denominator and numerator be multiplied by the expression in the denominator of the equation in question?
Thanks for your help.
Thanks for your help.
- krusta80
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In short, because it was the only way to get rid of the roots.HG10 wrote:Thanks for the explanation. Please let me know why you multiplied [root x - root ( x + y)] / [root x - root (x + y)] to get rid of the denominator, instead of multiplying the equation by [root x + root ( x + y)] / [root x + root ( x + y)]? Shouldn't the denominator and numerator be multiplied by the expression in the denominator of the equation in question?
Thanks for your help.
Remember, (a+b)*(a-b) = a^2 - b^2
(a+b)(a+b) = a^2 + 2ab + b^2
The 2ab, in this case, will still have a root in it.