If (x-12)2-(x-32)2=x+2, find x.

GATE 2021 CS (CS2) – Question 4

If $(x-\frac12)^2-(x-\frac32)^2=x+2$, find x.

Show answer and explanation

Correct answer: (B) 4

Use a²−b²=(a−b)(a+b). Here the difference of the two bracketed expressions is one and their sum is 2x−2. Therefore 2x−2=x+2, giving x=4. Thus B.

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