Question

if a,b,c are positive real number show that: √a^-1 b. √b^-1 c. √c^-1 a = 1​

Answer 1

Step-by-step explanation:

Assuming that (a+b+c) is not equal to zero.

Given that,

a+b-c/c=a-b+c/b=-a+b+c/a= sum of numerators/sum of denominators=1(A property of ratios)

Therefore,

a+b=2c

a+c=2b

b+c=2a

Therefore,

(a+b)(b+c)(c+a)/abc=2c.2a.2b/abc=8