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a^2=b+c b^2=c+a c^2=a+b find (1/a+1)+(1/b+1)+(1/c+1) please give detailed solution.

a^2=b+c
b^2=c+a
c^2=a+b
find (1/a+1)+(1/b+1)+(1/c+1)
please give detailed solution.

Grade:11

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
Subtract equation 1 from 2 :
a^2 - b^2 = b - a
(a+b) (a-b) = b-a
Hence, a + b = -1
Similarly,
b+c = -1
c+a = -1
a+b = -1
Now subtract any two derived equations :
b - a = 0, c - b = 0, a - c = 0
Hence, a = b = c = -1/2
Hence, now the given equation = 3/a+1 = 6
Answer = 6
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty

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