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If\frac{b+c-a}{a},\frac{c+a-b}{b},\frac{a+b-c}{c} are in AP then which of the following are in AP

Option: 1

a^{2},b^{2},c^{2}
 


Option: 2

\frac{1}{a},\frac{1}{b},\frac{1}{c}

 


Option: 3

2a,2b,2c


Option: 4

None of these


Answers (1)

best_answer

\frac{b+c-a}{a},\frac{c+a-b}{b},\frac{a+b-c}{c} are in Ap

\rightarrow \frac{b+c-a}{a}+2,\frac{c+a-b}{b}+2,\frac{a+b-c}{c}+2 are in AP

\rightarrow \frac{b+c+a}{a},\frac{c+a+b}{b},\frac{a+b+c}{c}  are in AP

Dividing each term by (a+b+c) will give a new AP

\rightarrow \frac{1}{a},\frac{1}{b},\frac{1}{c} are in AP

So,option(B) is correct

Posted by

Ajit Kumar Dubey

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