Question

q. 13 find x in terms of a, b, c​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

x = 0 and x = (2ab - bc - ac) / (a + b - 2c)

Step-by-step explanation:

Given : $\dfrac{a}{x - a} + \dfrac{b}{x - b} = \dfrac{2c}{x - c}$

→ $\dfrac{a(x - b) + b(x -a)}{(x - a)(x - b)} = \dfrac{2c}{x - c}$

Cross - multiplication, we get

→ (x - c) [a(x - b) + b(x - a)] = (2c) [(x - a)(x - b)]

→ (x - c) [ax - ab + bx - ab] = (2c) [x(x - b) - a(x - b)]

→ (x - c) [ax + bx - 2ab] = (2c) [x² - bx - ax + ab]

→ x(ax + bx - 2ab) - c(ax + bx - 2ab) = 2cx² - 2bcx - 2acx + 2abc

→ ax² + bx² - 2abx - acx - bcx + 2abc = 2cx² - 2bcx - 2acx + 2abc

Cancelling out common terms, we get

→ ax² + bx² - 2abx - acx - bcx = 2cx² - 2bcx - 2acx

→ ax² + bx² - 2cx² = - 2bcx + bcx - 2acx + acx + 2abx

→ ax² + bx² - 2cx² = - bcx - acx + 2abx

→ (a + b - 2c)x² = (- bc - ac + 2ab)x

→ (a + b - 2c)x² - (- bc - ac + 2ab)x = 0

→ (x) [(a + b - 2c)x - (- bc - ac + 2ab)] = 0

→ x = 0 and [(a + b - 2c)x - (- bc - ac + 2ab)] = 0

→ x = 0 and (a + b - 2c)x = 2ab - bc - ac

→ x = 0 and x = (2ab - bc - ac) / (a + b - 2c)