Question

please answer my question ??

Answer 1

Answer:

a + c = 2b

Step-by-step explanation:

Given Equation is (b - c)x² + (c - a)x + (a - b) = 0

On comparing with ax² + bx + c = 0,we get

a = (b - c), b = (c - a), c = (a - b).

Given that the roots are equal.

∴ D = 0

⇒ b² - 4ac = 0

⇒ (c - a)² - 4(b - c)(a - b) = 0

⇒ c² + a² - 2ac - 4[ab - b² - ac + bc] = 0

⇒ c² + a² - 2ac - 4ab + 4b² + 4ac - 4bc = 0

⇒ c² + a² + 2ac - 4ab - 4bc + 4b² = 0

⇒ (c + a)² - 4b(a + c) + 4b² = 0

⇒ (c + a)² - 2(2b)(a + c) + (2b)² = 0

⇒ [(c + a) - 2b]² = 0

⇒ (c + a) - 2b = 0

⇒ c + a = 2b.

Hope it helps!