If x^2 + y^2 = 100, what is the value of (x - y)^2 ?

Step 1: Analyse Question Stem

We know that \( x^2 + y^2\) = 100.

The value of \((x – y)^2\) is to be calculated.

\((x-y)^2\) = \(x^2\) +\( y^2\) – 2xy, we need the value of xy to be able to calculate the answer since \(x^2 + y^2\) is given as question data.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: x = \(\frac{48 }{ y}\)

Therefore, xy = 48. This is sufficient to calculate the value of \((x-y)^2\).

Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.

Statement 2: \(x^2−y^2\) = −28

From the question, \(x^2 + y^2\) = 100.

These two equations can be solved as simultaneous equations. Doing so, we get,
\(x^2\) = 36 and \(y^2\) = 64

Therefore, x = +6 or -6 and y = +8 or -8.

This means that we can different values for (x-y) and hence different values for \((x-y)^2\).
Statement 2 alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.