Question

If a(a+2)=a+b+c, b(b+2)=a+b+c, c(c+2)=a+b+c. What is 1/a+2 + 1/b+2 + 1/c+2

Answer 1

Answer:

hope it is helpful to you

Answer 2

Answer :

1/(a + 2) + 1/(b + 2) + 1/(c + 2) = 1

Solution :

★ Given :

• a(a + 2) = a + b + c

• b(b + 2) = a + b + c

• c(c + 2) = a + b + c

★ To find :

• 1/(a + 2) + 1/(b + 2) + 1/(c + 2) = ?

We have ;

=> a(a + 2) = a + b + c

=> (a + 2) = (a + b + c)/a

=> 1/(a + 2) = a/(a + b + c) -------(1)

Also ,

=> b(b + 2) = a + b + c

=> (b + 2) = (a + b + c)/b

=> 1/(b + 2) = b/(a + b + c) ----------(2)

Also ,

=> c(c + 2) = a + b + c

=> (c + 2) = (a + b + c)/c

=> 1/(c + 2) = c/(a + b + c) -----------(3)

Now ,

Adding eq-(1) , (2) and (3) , we have ;

=> 1/(a + 2) + 1/(b + 2) + 1/(c + 2)

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

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

= 1

Hence ,

1/(a + 2) + 1/(b + 2) + 1/(c + 2) = 1