If u^2 + (u−2v−1)^2 = −4v(u + v), then what is the value of u + 3v? Options

CAT 2018 Question Paper Shift 1 Solved Paper

Question : 79 of 100

Marks: +1, -0

u^2

(u−2v−1)^2

= −4v(u + v), then what is the value of u + 3v? Options

Solution:

u^{2}+(u-2 v-1)^{2}=-4 v(u+v)

⇒ u^{2}+u^{2}+4 v^{2}+1-4 u v+4 v-2 u+4 v u+4 v^{2}=0

⇒ 2 u^{2}-2 u+8 v^{2}+4 v+1=0

⇒ 2(u^{2}-u+\;{1}/{4})+2(4 v^{2}+2 v+\;{1}/{4})=0

⇒ 2(u-\;{1}/{2})^{2}+2(2 v+\;{1}/{2})^{2}=0

⇒ u-\;{1}/{2}=0 ; 2 v+\;{1}/{2}=0

{u}=\;{1}/{2} \;\text " and "\; {v}=-\;{1}/{4}

{u}+3 {v}=\;{1}/{2}-\;{3}/{4}=-\;{1}/{4}

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