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if (a-b)/c +(b-c)/a +(c+a)/b=1 then prove 1/a= 1/b + 1/c

if (a-b)/c +(b-c)/a +(c+a)/b=1 then prove 1/a= 1/b + 1/c

Grade:10

3 Answers

Ankit
104 Points
6 years ago
The question is not appropriate my dear friend. You are somewhere mistaken. It cannot be proved by any method.
Thank you
Hope u reconsider it
rupayan halder
16 Points
6 years ago
i have solved it
(a-b)/c +(b-c)/a +(c+a)/b=1
(a-b)/c +(b-c)/a +(c+a)/b=1+1-1
(a-b)/c+1 +(b-c)/a-1 +(c+a)/b-1=0
{(a-b)/c+1} +{(b-c)/a-1} +{(c+a)/b-1}=0
(a-b+c)/c +(b-c-a)/a +(c+a-b)/b=0
(a-b+c)/c -(-b+c+a)/a +(c+a-b)/b=0
(a-b+c)/c -(a-b+c)/a +(a-b+c)/b=0
(a-b+c)(1/c-1/a+1/b)=0
so {1/c-1/a+1/b}=0
=>1/a=1/b+1/c
(thanks for trying , i solved it few days ago )
Hritika Mahata
13 Points
2 years ago
(a-b)/c +(b-c)/a +(c+a)/b=1
(a-b)/c +(b-c)/a +(c+a)/b=1+1-1
(a-b)/c+1 +(b-c)/a-1 +(c+a)/b-1=0
{(a-b)/c+1} +{(b-c)/a-1} +{(c+a)/b-1}=0
(a-b+c)/c +(b-c-a)/a +(c+a-b)/b=0
(a-b+c)/c -(-b+c+a)/a +(c+a-b)/b=0
(a-b+c)/c -(a-b+c)/a +(a-b+c)/b=0
(a-b+c)(1/c-1/a+1/b)=0
 Either a-b+c=0 or (1/c-1/a+1/b)=0
(1/c-1/a+1/b)=0
1/c+1/b=1/a (proved)
 

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