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Explanation:

u2 + (u – 2v – 1)2 = −4v(u + v)

u2 + (u – 2v – 1)2 + 4v(u + v) = 0

(u – 2v – 1)2 + u2 + 4uv + 4v2 = 0

(u – 2v – 1)2 + (u + 2v)2 = 0

(u – 2v – 1)2 & (u + 2v)are both non-negative terms. Sum of two negative terms will be zero only when both the terms are equal to zero.

∴ u – 2v – 1 = 0 and u + 2v = 0

Solving the two equations, we get

u = 1/2 and v = -1/4

u + 3v = 1/2 - 3/4 = -1/4

Hence, option (b).

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