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
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.