I have posted this question 5 times and still no reply. These IITians cant solve simple polynomial questions. Please show that you are IITiansQ.1->a^2=b+cb^2=c+ac^2=a+bfind (1/a+1)+(1/b+1)+(1/c+1)Q.2-> If (1/b+c) +(1/c+a)=(2/a+b)find a^2+b^2please give the solution.

bharat bajaj IIT Delhi
9 years ago
Sorry for the delay,

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
Q2 : 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
`a^2 - b^2 = b - a(a+b) (a-b) = b-aHence, a + b = -1Similarly,b+c = -1c+a = -1a+b = -1Now subtract any two derived equations :b - a = 0, c - b = 0, a - c = 0Hence, a = b = c = -1/2Hence, now the given equation = 3/a+1 = 6Answer = 6Q2 : Take LCM ,(2c+a+b)/(a+c)(b+c) = 2/a+bCross multiply:a^2 + b^2 + 2ab + 2bc + 2ac = 2bc + 2ab + 2c^2 + 2acThis gives,a^2 + b^2 = 2. c^2`
`ThanksBharat Bajajaskiitians facultyIIT Delhi`