Question

a2/x-b2/y=0,a2b/x+b2a/y=a+b, solve for x

Answer 1

a²/x-b²/y=0---------1
a²b/x+b²a/y=a+b---2

Now from eq. 2,
=> ab(a/x+b/y)=a+b
=> a/x+b/y=a+b/ab ----- x b ( multiplying b)
=> ab/x+b²/y=a+b/a (after = b&b gets cancelled as one was in numerator and one was in denominator)


Equating eqs. 1 & 2,
a²/x-b²/y=0
ab/x+b²/y=a+b/a
----------------------------
=> a²/x + ab/x= 0 + a+b/a
=> a²+ab/x=a+b/a
=> a(a+b/x)=a+b/a. (a+b & a+b gets cancelled)
=> x=a²

Therefore, x=a² (ans)