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If a, b, C are distinct real numbers such that a:b+c=b:c+a then A) a, b,C are all positive numbers B) a, b, c are all negative C) a+b+c=0 D) ab+bc+ac+1=0

If a, b, C are distinct real numbers such that a:b+c=b:c+a then A) a, b,C are all positive numbers B) a, b, c are all negative C) a+b+c=0 D) ab+bc+ac+1=0

Grade:12

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 years ago
Considering a+c and b+c are not equal to zero
we cross multiply to get
a(a+c) = b(b+c)
a^2-b^2 = c(b-a)
(a+b)(a-b) = c(b-a)
which gives
a+b+c =0 \quad or \quad a=b

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