Math, asked by rchakraborty98, 9 months ago

If a/b+c = b/c+a = c/a+b, then each fraction is equal to​

Answers

Answered by BrainlicaLDoll
16

Given ratio : \rm \frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}

According to the property of ratio and proportions,

\mathsf{Each\:Ratio=\dfrac{Sum\:of\: antecedents}{Sum\:of\: consequents}}

Therefore,

If a + b + c ≠ 0, so the solution will be : -

\implies Each\:Ratio = \dfrac{a + b + c}{b + c + a + c + a + b} \\ \\ \\ \implies Each\:Ratio = \frac{a + b + c}{2a + 2b + 2c} \\ \\ \\ \implies Each\:Ratio = \dfrac{a + b +c }{2(a + b + c)} \\ \\ \\ \implies Each\:Ratio = \dfrac{1}{2}

If a + b + c = 0, then,

• b + c = - a

• a + b = - c

• a + c = - b

Therefore,

\implies Each\:Ratio = \dfrac{a}{b + c}=\dfrac{b}{a + c} = \dfrac{c}{a + b}

From above, values of b + c, a + b and a + c are - a , - b and - c respectively.

Hence,

\implies Each\:Ratio = \dfrac{a}{-a}=\dfrac{b}{-b} = \dfrac{c}{-c}

\implies Each\:Ratio = -1 = -1 = -1

Hence, proved that each ratio ( fraction ) is equal to \dfrac{1}{2} or - 1 .

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