CAT 2018 Slot 1 — QA Question 25
Solving Quadratic EquationsEasy
If u2 + (u−2v−1)2 = −4v(u + v), then what is the value of u + 3v?
Answer & solution
- A
1/2
-1/4
- C
0
- D
1/4
Solution
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)2 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).