gwen01 17.02.2009 12:28 It is given that $ a^2+b^2+(a+b)^2=c^2+d^2+(c+d)^2$. Prove that $ a^4+b^4+(a+b)^4=c^4+d^4+(c+d)^4$.
stephencheng 17.02.2009 13:06 Square both sides of the equation $ a^2+b^2+(a+b)^2=c^2+d^2+(c+d)^2$ and divide both sides by $ 2$ ,then we get the result.
ith_power 17.02.2009 13:24 stephencheng wrote: Square both sides of the equation $ a^2 + b^2 + (a + b)^2 = c^2 + d^2 + (c + d)^2$ and divide both sides by $ 2$ ,then we get the result. Umm.. What do we get then?
stephencheng 17.02.2009 14:07 ith_power wrote: Quote: Umm.. What do we get then? $ \frac {[a^2 + b^2 + (a + b)^2]^2}{2} = 2(a^2 + ab + b^2)^2 = 2a^4 + 4a^3 b + 6a^2 b^2 + 4a b^3 + 2b^4 = a^4 + b^4 + (a + b)^4$ Similarly for $ R.H.S.$