Question

real numbers ABC satisfying the equation a + b + c is equals to 26 1/a+1/b1/c=28 then the value of a/b+b/c+c/a+a/c+c/b+b/a is

Answer 1

Answer:

725

Step-by-step explanation:

$a + b + c = 26 --(A) \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 28\\\frac{ab + bc + ca}{abc} = 28 --(B)$

Now

$\frac{a}{b} + \frac{b}{c} + \frac{c}{a} + \frac{a}{c} +\frac{c}{b} + \frac{c}{b} \\\\\frac{ac(a + b) + ab(a+b) + bc(b+c)}{abc}$

$\frac{ac(26-b) + ab(26-c) + bc(26-a)}{abc}$

$\frac{26(ac + ab + bc) -3abc}{abc} \\\\\frac{26*28abc - 3abc}{abc}$

$\frac{725abc}{abc} \\\\725$

Hope this helps you!