algebra question

Question

If a/b=b/c then prove that (a+b+c)(a-b+c)=a²+b²+c²

Answer 1

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

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

(a+c)²-b²=

a²+2ac+c²-b².

a/b=b/c,

ac=b², so a²+2ac+c²-b²=a²+2b²+c²-b²=

a²+b²+c².

Therefore (a+b+c)(a-b+c)=a²+b²+c² QED