Are you one of those who feels Algebra is the worst nightmare that you could ever go through? To overcome the fear, incorporate the strategy of practisingCAT Previous Year Paperto your Online CAT Coaching.Now try this problem from CAT 2018 Question Paper before watching the video explaination
Question 16 : If u2 + (uโ2vโ1)2 = โ4v(u + v), then what is the value of u + 3v?
Given expression, u2 + (u โ 2v โ 1)2 = โ4v(u + v)
On expanding using (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca, we get
u2 + u2 + 4v2 + 1 - 4uv - 2u + 4v = - 4vu - 4v2
2u2 + 4v2 - 2u + 4v + 4v2 + 1 = 0
On rearranging and taking common we get,
2(u2 - u) + 2 (4v2 + 2v) = - 1
Add values on both sides to complete the squares inside parenthesis
2(u2 โ u + \\frac{1}{4})) + 2(4v2 + 2v + \\frac{1}{4})) = -1 + \\frac{1}{2}) + \\frac{1}{2})
2(u - \\frac{1}{2}))2 + 2(2v + \\frac{1}{2}))2 = 0
Since they both are squares, they canโt be negative
So, u - \\frac{1}{2}) = 0 and 2v + \\frac{1}{2}) = 0
u = \\frac{1}{2}) and v = โ\\frac{1}{4})
U+3v = \\frac{1}{2}) - \\frac{3}{4}) = -\\frac{1}{4})
The question is "If u2 + (uโ2vโ1)2 = โ4v(u + v), then what is the value of u + 3v?"
Choice D is the correct answer.
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