Let u and v be two positive real numbers satisfying the two equations u+v+uv=10 and u^2 +v^2=40. What is the value of integer closest to

u+v?

a)4

b)5

c)6

d)6

e)8

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- Jan 13th 2010, 04:49 AMTigerValue of Integers
Let u and v be two positive real numbers satisfying the two equations u+v+uv=10 and u^2 +v^2=40. What is the value of integer closest to

u+v?

a)4

b)5

c)6

d)6

e)8 - Jan 13th 2010, 05:21 AMDinkydoe
Observe that $\displaystyle 40 = (u+v)^2-2uv = (u+v)^2-2(10-(u+v))$

This gives:

$\displaystyle 60= (u+v)^2+2(u+v) $

Let $\displaystyle x = u+v$. Thus solve $\displaystyle 60 = x^2+2x$ for x and determine the digit closest to x.