Question

If a+b+c=1, a^2+b^2+c^2=9 and a^3+b^3+c^3=1, then the value of 1/a+1/b+1/c is

Answer 1

Good question.

$(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ac) \\ \\ = 1^2 = (a^2 + b^2 + c^2) + 2(ab + bc + ac) \\ \\ = 1 = 9 + 2(ab + bc + ac) \\ \\ \\ 2(ab + bc + ac) = 1 - 9 = - 8 \\ \\ ab + bc + ac = \frac{-8}{2} = -4$

$a^3 + b^3 + c^3- 3abc = (a + b + c)(a^2 + b^2 + c^2 - (ab + bc + ac)) \\ \\ = 1 - 3abc = (1)(9 - (-4)) \\ \\ = 1 - 3abc = 1 \times 13 = 13 \\ \\ 1 - 13 = 3abc = -12 \\ \\ abc = \frac{-12}{3} = -4$

$\\ \\ \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{ab + bc + ac}{abc} \\ \\ = \frac{-4}{-4} = \bold{1}$

∴ 1 is the answer.

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Answer 2

Answer:

the above answer is correct ....please mark the avobe as brainiest