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

Answer 1

Answer:

724

Step-by-step explanation:

Let's write x = a + b + c and y = 1/a + 1/b + 1/c (notice I'm supposing that the second expression in the question was meant to be this, with a "+" between 1/b and 1/c).

Let's write z = a/b + b/c + c/a + a/c + c/b + b/a.

We have x = 26 and y = 28.  We need to find z.

Terms like those in the expression for z look exactly like what we'd get if we multiply things like a, b and c, by things like 1/a, 1/b and 1/c.  So it's tempting to try multiplying x and y.  Sure enough, when we do this and expand, we get

x y = (a)(1/a) + (b)(1/b) + (c)(1/c) + z  = 1 + 1 + 1 + z = 3 + z.

We know x and y, so this becomes

3 + z = x y = 26 x 28

and so

z = 26 x 28 - 3 = 727 - 3 = 724