Question

If x = –y and y > 0, which of the following is wrong?

Options

• x²y > 0

• x + y = 0

• xy < 0

• `1/x - 1/y = 0`

Answer 1

`bb(1/x - 1/y = 0)`

Explanation:

a. x²y > 0 (Correct statement): Since x is a non-zero negative number, its square x² is positive. Multiplying a positive number (x²) by another positive number (y) always results in a positive value (> 0).

b. x + y = 0 (Correct statement): If you add y to both sides of the given equation x = – y, it directly simplifies to x + y = 0.

c. xy < 0 (Correct statement): Since x is negative and y is positive, multiplying them together (opposite signs) always results in a negative value (< 0).

d. `1/x - 1/y = 0` (Wrong statement): Substituting x = – y into this expression gives:

`1/(-y) - 1/y = -1/y - 1/y = -2/y`

Since `y > 0 - 2/y` cannot equal 0. It will always be a negative number.