chetan2u wrote:

DH99 wrote:

What is the value of x?

1. √ x = x-2

2. x is not equal to 1.

Hi..

1) √x=x-2

Square both sides

\(x=x^2-4x+4.....x^2-5x+4=0....x^2-4x-x+4=0.........(x-4)(x-1)=0\)

So x can be 4 or 1..

Substitute in equation and see if values are valid.

A) 2

√4=4-2=2.... Valid

B) 1

√1=1-2=-1..... Not valid

SQUARE Root has to be POSITIVEOnly possible value :- 4

Sufficient

2) X is not 1..

Nothing much.

But only to tempt you to click C....the C trapInsufficient

Thanks Chetan

Answer to this question teach us a very good lesson. Whenever we are doing squire on both the sides of the equation to solve it, always check putting the solution back into the equation to see if the value really satisfy the original equation.

For example, in this case by solving (by squiring both the sides) equation given in option 1, we get solution as 1 and 4, however putting back the value in the original equation clearly shows value=1 do not satisfy the original equation.

The reason for this is that for the simplicity we are doing squire on both the sides, but mathematically it produced a fundamentally different equation as compared to the original equation.

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