Question

the solution of the equation m/x+n/y=a and n/x+m/y=b​

Answer 1

Answer:

the answer to this equation is or can be x²

Answer 2

Answer:

Given equations are : (1) m/x + n/y = a

(2) n/x + m/y = b

let 1/x = u & 1/y = v

then, m/x+n/y = mu+nv

And, n/x + m/y = nu+mv

so, new equations are : (1) mu+nv = a or, mu+nv - a = 0 (2) nu + mv = b or, nu+mv-b = 0

Solving for u and v by cross-multiplication method :

u = (b1c2-- b2c1) ÷ (a1b2 - a2b1)

=》u= [n×(-b) --m × (-a)]÷ (m×m - n×n )

=》u = (-bn+am)÷(m^2-n^2)

=》u= (am-bn)÷(m^2-n^2)

Now, u= 1/x

so, x = (m^2 - n^2)÷(am-bn)

similarly,

v = (c1a2 - c2a1 )÷(a1b2 - a2b1)

=》v= [(-a)×n - (-b)×m] ÷(m×m -n×n )

=》v=(bm- an)÷(m^2 -n^2)

Now, v= 1/y

so, y = (m^2 - n^2)÷(bm-an)

Hence, x= (m^2 - n^2)÷(am-bn) &

y = (m^2 - n^2)÷(bm-an)