1 a 1 b 1 c are in ap


Asked by admin @ in Math viewed by 332 People


If 1/a , 1/b , 1/c are in AP. Then PT. b+c/a , c+a/b, a+b/c are in AP​

Answered by admin @



GIVEN :

Terms 1/a , 1/b , 1/c are in A.P.

TO PROVE :

(b+c)/a , (c+a)/b , (a+b)/c are in A.P.

SOLUTION :

• According to the question –

=> 1/a , 1/b , 1/c are in A.P.

• Now multiply with (a + b + c) —

 \\  \implies \:  \frac{(a + b + c)}{a}  \: , \:  \frac{a + b + c}{b}  \: , \:  \frac{a + b + c}{c}  \:  \: are \:  \: in \:  \: A.P.  \\

• Now , we should write this as –

 \\  \implies \:  \frac{(b + c)}{a}  + 1 \: , \:   \frac{(c + a)}{b}  + 1 \: , \:  \frac{(a + b)}{c}  + 1 \:  \: are \:  \: in \:  \: A.P. \:   \\

• Now subtract 1 from all terms –

 \\  \implies \:  \frac{b + c}{a}  \: , \:  \frac{c + a}{b}  \: , \:  \frac{a + b }{c}  \:  \: are \:  \: in \:  \: A.P. \:  \\

(Hence proved)


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