Question

X÷a +y÷b =ab
X/a²+y÷b²=2a²b²

Answer 1

x = a^2, y = b^2

Step-by-step explanation:

Given that,

x/a + y/b = a + b; x/a^2 + y/b^2 = 2

Solving the equation x/a + y/b = a + b

⇒ bx + ay = ab(a + b)  ...(i)

Solving the equation x/a^2 + y/b^2 = 2,

⇒ b^2x + a^2y = 2a^2b^2   ...(ii)

Now,

b * (i) - (ii)

⇒ [b^2x + aby] - [(b^2x + a^2y)] = ab^2(a + b) - 2a^2b^2

⇒  b^2x + aby - b^2x - a^2y = a^2b^2 + ab^3 - 2a^2b^2

⇒  aby - a^2y = ab^3 - a^2b^2

⇒ y (b-a)a = ab^2(b- a)

⇒  y = ab^2(b - a)/a(b-a)

∵   y = b^2

While putting the value of y in equation (ii),

b^2x + a^2y = 2a^2b^2

⇒ b^2x = 2a^2b^2 - a^2b^2

⇒ x = (a^2b^2)/b^2

∵ x = a^2