Discussion Problem_(24)

[duck]

Q1)  Let a,b and c be distinct real numbers such that
a^2-b = b^2-c = c^2-a.
Find the value of (a+b)*(b+c)*(a+c).

[anmol]

1

[MI]

1

[Xiang]

1

[Sumit]

Answer=1
Solution.
First Take
a^2-b=b^2-c.
->a^2-b^2=b-c
->(a+b)(a-b)==b-c---------1)

Similarly from b^2-c = c^2-a.
we get (b+c)(b-c)=c-a-------2)

n From a^2-b=c^2-a..
we get (a+c)(a-c)=b-a--------3)

now multiply 1),2) n 3)
we will get (a+b)*(b+c)*(a+c)=1

[duck]

Cool. Correct answer.. :)