Question

a+b+c=3
a^2+b^2+c^2=6
1/a+1/b+1/c=1

find values of a , b and c. ​

Answer 1

$a + b + c = 3$

${a}^{2} + {b}^{2} + {c}^{2} = 6$

$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1$

$Now \:$

$( a+ b +c )^{2} = 9$

${a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) = 9$

$6 + 2(ab +bc +ca ) = 9$

$ab + bc + ca = \frac{3}{2}$

$now \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1$

$\frac{ab + bc + ca}{abc} = 1$

$abc = ab + bc + ca = \frac{3}{2}$