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If (1/b+c) +(1/c+a)=(2/a+b) find a^2+b^2 Please post the full solution.

If (1/b+c) +(1/c+a)=(2/a+b)
find a^2+b^2
Please post the full solution.

Grade:12

2 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
Take LCM ,
(2c+a+b)/(a+c)(b+c) = 2/a+b
Cross multiply:
a^2 + b^2 + 2ab + 2bc + 2ac = 2bc + 2ab + 2c^2 + 2ac
This gives,
a^2 + b^2 = 2. c^2
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty
mycroft holmes
272 Points
7 years ago
1/(b+c) - 1/(a+b) = 1/(a+b) - 1/(a+c) gives (a-c)/(a+b)(b+c) = (c-b)/(a+b)(a+c) or (a-c)(a+c)/(a+b)(b+c)(c+a) = (c-b)(c+b)/(a+b)(b+c)(c+a) or a^2-c^2 = c^2-b^2 or a^2+b^2 = 2c^2

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