Question

if 1/a + 1/b + 1/c=1/(a+b+c) where a+b+c#0,abc#0 what is the value of (a+b)(b+c)(c+a)?
a)equals 0
b)greater than 0
c)less than 0
d)cannot be determined

Answer 1

Given: 1/a + 1/b + 1/c = 1 / (a+b+c)

To find: The value of (a+b)(b+c)(c+a)?

Solution:

• Now we have given the equation as 1/a + 1/b + 1/c = 1 / (a+b+c).

• We have also given that a + b + c ≠ 0, abc ≠ 0

• Now we can write the equation as:

                     1/a + 1/b = 1 / (a+b+c) - 1/c

• Taking LCM, we get:

                     ( b + a ) / ab = ( c - ( a + b + c ) ) / c( a + b + c )

• Now cross multiplying, we get:

                      c( a + b + c ) x ( b + a ) = -ab x ( a + b )

                     ( a + b ) x ( ca +cb +cc + ab ) = 0

                     ( a + b ) x ( ca + cc + cb + ab) = 0

                     ( a + b ) x ( b + c ) x ( c + a ) = 0

Answer:

               So the value of ( a + b ) x ( b + c ) x ( c + a ) is 0.

Answer 2

Step-by-step explanation: