Just require a substitution!

Algebra Level 4

$\begin{cases}5 x\left(1+\frac { 1 }{ { x }^{ 2 }+y^{ 2 } } \right)=12\\ 5y \left(1-\frac { 1 }{ { x }^{ 2 }+{ y }^{ 2 } } \right)=4 \end{cases}$ If $x=a$ and $y=b$ satisfy the above equations simultaneously for $a>b>0$ , then find $a+b$ .

The answer is 3.

1 solution

Kushal Dey
Mar 25, 2020

Let z=x+iy, where i is the square root of -1. Now multiplying second equation with i and adding to the first equation, you have, 5z+5/z=12+4i, which yeilds a quadratic equation in z involving complex coefficients.(Hope you can deal with complex numbers.)

Just require a substitution!

The answer is 3.

1 solution

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