maths2題,,緊急plz

Q.1
　2a²+2b²+2c²-2ab-2bc-2ca
≡ (a²-2ab+b²) + (b²-2bc+c²) + (c²-2ca+a²)
≡ (a-b)² + (b-c)² + (c-a)²
Putting a=2006, b=2007, c=2008, then we have:
　2(2006)²+2(2007)²+2(2008)²-2(2006)(2007)-2(2007)(2008)-2(2006)(2008)
= (2006-2007)² + (2007-2008)² + (2008-2006)²
= 1² + 1² + 2²
= 6

Q.2
x² y + y² = 30
y (x² + y) = 30

Consider the factors of 30:
　30 = 1 X 30
　30 = 2 X 15
　30 = 3 X 10
　30 = 5 X 6
　30 = (-1) X (-30)
　30 = (-2) X (-15)
　30 = (-3) X (-10)
　30 = (-5) X (-6)

When y = 1, x² = 30-1 = 29, no solution for x.
When y = 2, x² = 30-2 = 28, no solution for x.
When y = 3, x² = 30-3 = 27, no solution for x.
When y = 5, x² = 30-5 = 25, x = ±5.
When y = 6, x² = 30-6 = 24, no solution for x.
When y = 10, x² = 30-10 = 20, no solution for x.
When y = 15, x² = 30-15 = 15, no solution for x.
When y = 30, x² = 30-30 = 0, x = 0.

When y = -1, x² = 30+1 = 31, no solution for x.
When y = -2, x² = 30+2 = 32, no solution for x.
When y = -3, x² = 30+3 = 33, no solution for x.
When y = -5, x² = 30+5 = 35, no solution for x.
When y = -6, x² = 30+6 = 36, x = ±6.
When y = -10, x² = 30+10 = 40, no solution for x.
When y = -15, x² = 30+15 = 45, no solution for x.
When y = -30, x² = 30+30 = 60, no solution for x.

So, the solution sets are
(x, y) = (±5, 5), (±6, -6), (0, 30)

2007-02-24 21:33:27 補充：
================================請大家評評理：http://hk.knowledge.yahoo.com/question/?qid=7007022203731答案３,４,５都是正確的，而且都有steps，怎麼目前「票數最高」的不是最早答的答案３，而是最遲答的答案５？

1. Put x = 2006, so
2x^2 + 2(x+1)^2 + 2(x+2)^2 - 2x(x+1) - 2(x+1)(x+2) - 2(x+1)(x+2)
= [x^2 - 2x(x+1) + (x+1)^2] + [x^2 - 2x(x+2) + (x+2)^2] + [(x+1)^2 - 2(x+1)(x+2) + (x+2)^2]
= [x - (x+1)]^2 + [x - (x+2)]^2 + [(x+1) - (x+2)]^2
= [1]^2 + [2]^2 + [-1]^2
= 1 + 4 + 1
= 6

2. don't know