Question

If a + b + c = 4, a2 + b2 + c 2= 11 and
1/a+1/b+1/c=1
where a, b and call are non-zero, then the value of abc
is:
5/2
O
3/2
07
3

Answer 1

Answer:

$a + b + c = 4\\\\a^{2} + b^{2} + c^{2} = 11\\\\\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1$

finding the value of bc + ac + ab

$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca)\\\\(4)^{2} - 11 = 2(ab + bc + ac)\\\\\frac{16 - 11 }{2} = ab + bc + ac\\\\ab +bc + ac = \frac{5}{2}$

now,

$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1\\\\\frac{bc + ac + ab}{abc} = 1\\\\\frac{\frac{5}{2}}{abc} = 1\\\\=> abc = \frac{5}{2}$