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Question Number 212179 by cherokeesay last updated on 05/Oct/24

	Answered by cemoosky last updated on 05/Oct/24

	$x = 6.6$
	Answered by mr W last updated on 06/Oct/24

	Commented by mr W last updated on 06/Oct/24

	$A D : y = m x$ $y = 1 - x$ $1 - x_{B} = {m x}_{B} \Rightarrow x_{B} = \frac{1}{1 + m}$ $y = - 1 + x$ $- 1 + x_{C} = {m x}_{C} \Rightarrow x_{C} = \frac{1}{1 - m}$ $\frac{a}{b} = \frac{x_{B}}{x_{C} - x_{B}} = \frac{\frac{1}{1 + m}}{\frac{1}{1 - m} - \frac{1}{1 + m}} = \frac{1 - m}{2 m}$ $\Rightarrow m = \frac{b}{2 a + b}$ $\frac{x}{a} = \frac{2 - x_{C}}{x_{B}} = \frac{2 - \frac{1}{1 - m}}{\frac{1}{1 + m}} = \frac{(1 - 2 m) (1 + m)}{1 - m}$ $x = \frac{(1 - 2 m) (1 + m) b}{2 m}$ $\Rightarrow x = \frac{(a + b) (2 a - b)}{2 a + b}$ $= \frac{(6 + 4) (2 \times 6 - 4)}{2 \times 6 + 4} = 5$
	Commented by cherokeesay last updated on 06/Oct/24

	$t h a n k y o u m a s t e r!$
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