Harder 2unit Maths Question (1 Viewer)

[mrzeidan1]

Hey, question is from Cambridge Year 11 book

Prove a=b=c=d for the following expression

(a+b)^2 + (b+c)^2 + (c+d)^2 = 4(ab+bc+cd)

Thanks

 

[Mark576]

I'll have a go:

First expand:

a^2 + 2ab + b^2 + b^2 + 2bc + c^2 + c^2 + 2dc + d^2 = 4ab +4bc +4cd

Collect like terms:

a^2 - 2ab + b^2 + b^2 - 2bc + c^2 + c^2 - 2dc + d^2 = 0

Factorise the perfect squares:

(a - b)^2 + (b - c)^2 + (c - d)^2 = 0

Since the sum of the squares equals zero each individual square must equal 0:

Therefore: a = b = c = d

Hope i'm right

 

[SoulSearcher]

Yeah, you're right there

 

[fishy89sg]

noice job mang

 

[karnoganguli]

i encountered the same question a few months ago... took me a day. nice work mark

 

[amisha_amisha]

Omgg...this is like a foreign language to me! LOL

 

[SoulSearcher]

Just some expansions and factorisations