Question

Hey, can anyone help with this question, it’s 10th grade Quadratic Equations chapter.

Answer 1

Refer image for your solution

Answer 2

if a quadratic equation Ax² + Bx + C = 0 has equal roots then B² - 4AC = 0

in the above question we can notice that B = 2mnc , A = (1 + m²)n² , C = c² - a²

substituting the above values in B² - 4AC = 0 we get

⇒ 4m²n²c² - 4n²(1 + m²)(c² - a²) = 0

4n² is taken common and made zero

⇒ m²c² - (c² - a² + m²c² - m²a²) = 0

⇒ m²c² - c² + a² - m²c² + m²a² = 0

⇒ m²a² + a² = c²

⇒ a²(m² + 1) = c²