Question

X/a + Y/b = a+b ;. X/ a^2 + Y/b^2 = 2,a,b≠0​

Answer 1

Solution :-

Given pair of linear equations :

• x/a + y/b = a + b ---- eq(1)
• x/a² + y/b² = 2 ---- eq(2)

x/a² + y/b² = 2

Multiplying through by 'a'

⇒ x/a + ay/b² = 2a --- eq(3)

Subtracting eq(1) from eq(3)

⇒ x/a + ay/b² - ( x/a + y/b ) = 2a - ( a + b)

⇒ x/a + ay/b² - x/a - y/b = 2a - a - b

⇒ ay/b² - y/b = a - b

Taking LCM

⇒ ( ay - by ) / b² = a - b

⇒ ay - by = b²(a - b)

⇒ y(a - b) = b²(a - b)

⇒ y = b²(a - b) / (a - b)

⇒ y = b²

Substituting y = b² in eq(1)

⇒ x/a + y/b = a + b

⇒ x/a + b²/b = a + b

⇒ x/a + b = a + b

⇒ x/a = a + b - b

⇒ x/a = a

⇒ x = a * a

⇒ x = a²

Therefore the value of x is a² and y is b².