Helium wrote:
If \(XY ≠ 0\) and \(X^3Y = XY^3\), then which of the following must be true?
I) \(|X| = -|Y|\)
II) \(|X| = |Y|\)
III) \(X = Y = 1\)
A) None
B) II only
C) III only
D) I and II only
E) I, II, and III
\(X^3Y = XY^3\)
\(X^3Y - XY^3 = 0\)
\(XY (X^2 - Y^2) = 0\)
\(XY (X - Y) (X+Y) = 0\)
Now XY != 0(given) so X^2 = Y^2
I) \(|X| = -|Y|\)
Now this inequality can show 4 cases, We can't say anything about XY(This can be +ive or -ive), i wont go with this. Not sufficient
X= - Y, X= -(-Y), -X = -Y and -X = - (-Y)
II) \(|X| = |Y|\)
This is always true, square root of X^2 = Y^2 => |X| = |Y|
III) \(X = Y = 1\)
Not necessary, what if the value is different
Answer B
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Quote which i can relate to.
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