Suppose that ^@ a, b, c ^@ are distinct numbers such that ^@ ( c - b )^2 - 4( c - a )( a - b ) = 0, ^@ find the value of ^@ \dfrac{ c - a }{ a - b }. ^@


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Answer:

^@ 1 ^@

Step by Step Explanation:
  1. Given, ^@ (c - b)^2 - 4(c - a)(a - b) = 0, ^@ we need to find the value of ^@ \dfrac{ c-a } { a-b }. ^@
  2. ^@ \begin{align} & (c - b)^2 -4(c - a)(a - b) = 0 \\ \implies & (c - a + a - b)^2 -4(c - a)(a - b) = 0 \\ \implies & \Big( (c - a) + (a - b) \Big)^2 -4(c - a)(a - b) = 0 \\ \implies & (c - a)^2 + (a - b)^2 + 2(c - a)(a - b) -4(c - a)(a - b) = 0 \\ \implies & (c - a)^2 + (a - b)^2 - 2(c - a)(a - b) = 0 \\ \implies & \Big( (c - a) - (a - b) \Big)^2 = 0 \\ \implies & (c - a) - (a - b) = 0 \\ \implies & (c - a) = (a - b) \\ \implies & \dfrac{ c - a } { a - b } = 1 \end{align} ^@

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