Question

If x = −y and y > 0, which of the following is wrong?
(a) $x^{2}y>0$
(b) $x+y=0$
(c) $xy<0$
(d) $\frac{1}{x}-\frac{1}{y}=0$

Answer 1

The correct option is (d).

Given:
x = −y and y > 0
Now, we have:
(i) x²y
On substituting x = −y, we get:
(−y)²y = y³ > 0 (∵ y > 0)
This is true.

(ii) x + y
On substituting x = −y, we get:
(−y) + y = 0
This is also true.

(iii) xy
On substituting x = −y, we get:
(−y) y = −y² < 0 (∵ y > 0)
This is again true.

(iv) $\frac{1}{x}-\frac{1}{y}=0$
$\Rightarrow \frac{y-x}{xy}=0$
On substituting x = −y, we get:
$\frac{y-\left(-y\right)}{\left(-y\right)y}=0\Rightarrow \frac{2y}{-y^2}=0\Rightarrow 2y=0\Rightarrow y=0$
Hence, from the above equation, we get y = 0, which is wrong.