Question

Solve for x and y:

`x/a + y/b = a + b, x/(a^2) + y/(b^2) = 2`

Answer 1

The given equations are

`x/a + y/b = a + b`   ...(i)

`x/(a^2) + y/(b^2) = 2`   ...(ii)

Multiplying (i) by b and (ii) by b² and subtracting, we get

`(bx)/a - (b^2x)/(a^2) = ab + b^2 - 2b^2`

⇒ `(ab - b^2)/(a^2)x = ab - b^2`

⇒ `x = ((ab - b^2)a^2)/(ab - b^2) = a^2`

Now, substituting x = a² in (i) we get

`(a^2)/a + y/b = a + b`

⇒ `y/b = a + b - a = b`

⇒ y = b²

Hence, x = a² and y = b².