Suppose ^@ a \ne 0, b \ne 0, c \ne 0 ^@ and ^@ \dfrac{ a } { b } = \dfrac{ b } { c } = \dfrac{ c } { a } .^@ Find the value of ^@ \dfrac{ a - b + c } {a + b - c }. ^@


Answer:

^@ 1 ^@

Step by Step Explanation:
  1. We need to find the value of ^@ \dfrac{ a - b + c }{ a + b - c } . ^@
    Let ^@ \dfrac{ a } { b } = \dfrac{ b } { c } = \dfrac{ c } { a } = k ^@
  2. From ^@ \dfrac{ a } { b } = \dfrac{ b } { c } = \dfrac{ c } { a } = k, ^@ we get
    ^@ \begin{align} & a = bk, b = ck, \text{ and } c = ak \\ \implies & a = ak^3 \\ \implies & k^3 = 1 \\ \implies & k = 1 \\ \implies & a = b = c \end{align} ^@
  3. Now,
    @^ \dfrac{ a - b + c } {a + b - c } = \dfrac{ a - a + a } { a + a - a } = 1 @^

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