Question

If a:b=b:c then show that (a2+ab+ b2)(b2-bc+c2)=a2b2+b2c2+c2a2.

Answer 1

Answer: (a2+ab+ b2)(b2-bc+c2)=a2b2+b2c2+c2a2

Step-by-step explanation:

a:b = b:c

then ac = b^2 ......... eq 1

now (a2+ab+b2)(b2-bc+c2) = a2b2 + b2c2 + a2c2 - a2bc + ab3 -ab2c + abc2 + b4 - b3c

by using eq 1

b4 = ab2c (replace ac with b2) ==> b4 = b4

b3c = abc2 (replace b2 with ac)

ab3 = a2bc

these 6 terms will cut one another

so finally we have left with a2b2 + b2c2 + a2c2