Question

solve class 10 ques 29

Answer 1

Answer:

2b = a + c

Step-by-step explanation:

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

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

Given that roots are real.

∴ D = 0

b² - 4ac = 0

⇒ (c - a)² - 4(b - c)(a - b) = 0

⇒ (c + a² - 2ac) - 4(ab - b² - ca + bc) = 0

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

⇒ a² + 4b² + c² - 4ab - 4bc + 2ac = 0

⇒ a² + (-2b)² + c² + 2(a)(-2b) + 2(-2b)(c) + 2(c)(a) = 0

⇒ (a - 2b + c)² = 0

⇒ a - 2b + c = 0

⇒ -2b = -a - c

⇒ -2b = -(a + c)

⇒ 2b = a + c.

Hope it helps!