Question

Refer to the attachment.

COULD ANYONE EXPLAIN??

THANKS!!

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Answer 1

[0010001111]... Hello User... [1001010101]
Here's your answer...

In each of the sums, you are getting 3 values. Out of them, only two are correct. Here's the reason.
In the first sum, we'll try putting -1 as x's value in the root part of the equation. And we'll assume the root part to be y.
Then...
$\sqrt{2 \times ( - 1) - 1} = y \\ y = \sqrt{ - 2 - 1} = \sqrt{ - 3}$
If this is the value of y, then y² will be -3. However, there is no real value whose square is negative. Try it. The square of 2 is 4. The square of -2 is also 4. Since this value of y is not real, its an imaginary number. And imaginary numbers cannot be the solutions to equations. That's why -1 cannot be a solution to the equation.
The same reason applies to the rest of the questions.
In the second question, if x=-2,
$y = \sqrt{ - 2 + 1} = \sqrt{ - 1}$
Again, y² will be -1. And the the equation becomes imaginary. So -2 is not a solution.
In the third question, x=3
$y = \sqrt{2 - 3} = \sqrt{ - 1}$
Again, the same reason.

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