Does (x − y)^2 = 100 ? (1) x^2 + y^2 = 52 (2) x + y = 2

Solution

Step 1: Analyse Question Stem

• We need to find if \((x-y)^2 = 100\)

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

• \((x-y)^2 = x^2 + y^2 – 2xy ⟹ (x-y)^2 = 52 – 2xy\)
• However, we don’t know the value of 2xy.

• With this statement, we cannot find the value of x-y, therefore we cannot find \((x-y)^2\)

Step 3: Analyse Statements by combining.

• From statement 1: \(x^2 + y^2 = 52….Eq.(i)\)

o And \((x-y)^2 = 52 – 2xy……Eq.(ii)\)
• From statement 2: \( x+ y = 2\)

o \( (x+y)^2 = 4 ⟹ x^2 + y^2 + 2xy = 4…….Eq.(iii)\)
• On combining both statements:

o Subtracting Eq.(i) from Eq.(iii) we get,

 \(2xy = 4-52 = -48\)
o By substituting the value of 2xy from the above equation into Eq.(ii), we can easily find the value of \((x-y)^2\)