(x+2y)^(2)=10xy
(x-2y)^(2)=2xy
x+2y=(10xy)^(1/2)
x-2y=(2xy)^(1/2)
x+2y/x-2y=sqrt10*sqrt(xy)/sqrt2*sqrt(xy)
sqrt(xy)'s cancel and you're left with sqrt10/sqrt2=sqrt5*sqrt2/sqrt2=sqrt5 (E)
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Algebra
Source: Beat The GMAT — Problem Solving |
Square numerator and denominator(since we are given value for x^2+4y^2)
x^2+4y^2+4xy / x^2+4y^2-4xy
= 6xy+4xy/6xy-4xy
= 5
Since we squared it now take the square root
sqrt(5)
Hence E
x^2+4y^2+4xy / x^2+4y^2-4xy
= 6xy+4xy/6xy-4xy
= 5
Since we squared it now take the square root
sqrt(5)
Hence E
