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If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in AP., prove that a, b, c are in AP.
If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in AP., prove that a, b, c are in AP.
Arithmetic Progressions | CBSE | Class 11 | Exercise 19.5 | Maths | RD Sharma
If a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in AP., prove that a, b, c are in AP.

Answer:

Given,

a(1/b + 1/c), b(1/c + 1/a), c(1/a + 1/b) are in AP

Also, a(1/b + 1/c) + 1, b(1/c + 1/a) + 1, c(1/a + 1/b) + 1 are in AP

Let us take LCM for each expression,

(ac+ab+bc)/bc , (ab+bc+ac)/ac, (cb+ac+ab)/ab are in AP

1/bc, 1/ac, 1/ab are in AP

Multiply numerator with ‘abc’, we get

abc/bc, abc/ac, abc/ab are in AP

∴ a, b, c are in AP.

Thus, proved.

i

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