Question

a2/x - b2/y=0
a2b/x + b2a/y = a+b
solve and find x and y

Answer 1

Heya....


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)

Answer 2

(a^2)/x - (b^2)/y = 0 __1
(a^2)b/x - (b^2)a/y = (a+b) __2
from equation 1
(a^2)/x = (b^2)/y. ____3
now putting the value of (a^2)/x in equation 2
(b^2)b/y - (b^2)a/y = (a+b)
taking (b^2)/y common
(b^2)/y [b- a] = a+ b
y = (b^2) (b- a)/ (a + b)
using 3rd equation we get
(a^2)/x = (a+ b)/(b- a)
x = (a^2)(b- a)/(a+b)

Hence the values of x and y are x = (a^2)(b- a)/(a+b) and y = (b^2) (b- a)/ (a + b)

Hope it helps!!!!