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Bunuel
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x (1-y) (1+y) = \(x(1-y^2)\)

Statement 1

\(x^2 = x\)

=> \(x^2 - x = 0 => x(x-1) = 0 \)

=> x = 0 or 1

If x = 0, then the value of the expression = 0

If x =1, the value of expression = \(1-y^2\) & we don't know the value of y

Hence statement 1 is insufficient.

Statement 2

\(y^2 = x \)

=> Given expression will become x (1-x) & we don't know the value of x

Hence, statement 2 is insufficient


Statement 1 + Statement 2

From Statement 1 x = 0 or 1
from statement 2 expression becomes x(1-x)

at x =0 & 1 the value of the expression is 0.

Hence, statement 1 & statement 2 both are required.

Option C should be the answer.
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What is the value of x(1−y)(1+y)x(1−y)(1+y) ?

From 1, (x)(x-1) = 0 --> (x = 0) or (x = 1)
So, A is not sufficient, BCE

From 2, (y*y)(1-y)(1+y) = ?
(y^2)(1-y^2) = ?
Cannot be answered., So C Or E

From 1 and 2,
(0)(1-0) = 0
(1)(1-1) = 0
So C.
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