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For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the
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15 Mar 2021, 10:40
15 Mar 2021, 10:40
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For all real numbers \(x\) and \(y\), let x#y = \((xy)^2 − x + y^2\) . What is the value of y that makes x # y equal to \(–x\) for all values of \(x\) ?
(A) 0
(B) 2
(C) 5
(D) 7
(E) 10
(A) 0
(B) 2
(C) 5
(D) 7
(E) 10
Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the
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15 Mar 2021, 19:14
15 Mar 2021, 19:14
1
x#y = \((xy)^2 − x + y^2\) = -x
\(x^2y^2\) -x + \(y^2\) = -x
\(x^2y^2\) + \(y^2\) = 0
\(y^2\) \((x^2+1)\) = 0
Now \((x^2+1)\) will always be greater than or equal to 1.
So y has to be 0
Answer A
\(x^2y^2\) -x + \(y^2\) = -x
\(x^2y^2\) + \(y^2\) = 0
\(y^2\) \((x^2+1)\) = 0
Now \((x^2+1)\) will always be greater than or equal to 1.
So y has to be 0
Answer A
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Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the
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15 Mar 2021, 23:30
15 Mar 2021, 23:30
Carcass wrote:
For all real numbers \(x\) and \(y\), let x#y = \((xy)^2 − x + y^2\) . What is the value of y that makes x # y equal to \(–x\) for all values of \(x\) ?
(A) 0
(B) 2
(C) 5
(D) 7
(E) 10
(A) 0
(B) 2
(C) 5
(D) 7
(E) 10
\(x # y = -x\)
\((xy)^2 − x + y^2 = -x\)
\(x^2y^2 + y^2 = 0\)
\(y^2(1 + x^2) = 0\)
\(y^2 = \frac{0}{(1 + x^2)} = 0\)
\(y = 0\)
Hence, option A
