Comparison inequality size 1. Compare the size of X & # 178; + Y & # 178; + 5 and 2 (y-2x) 2. When x ≠ - 1, compare the size of 5x & # 178; + 6x-8 and 3x & # 178; + 2x-10

Comparison inequality size 1. Compare the size of X & # 178; + Y & # 178; + 5 and 2 (y-2x) 2. When x ≠ - 1, compare the size of 5x & # 178; + 6x-8 and 3x & # 178; + 2x-10

1、x²+y²+5-2(y-2x)
=x²+4x+4+y²-2y+1
=(x+2)²+(y-1)²
Because: (x + 2) &# 178; ≥ 0, (Y-1) &# 178; ≥ 0
So we can get: X & # 178; + Y & # 178; + 5-2 (y-2x) ≥ 0
Namely: X & # 178; + Y & # 178; + 5 ≥ 2 (y-2x)
2、5x²+6x-8-(3x²+2x-10)
=2x²+4x+2
=2(x+1)²
When x ≠ - 1, x + 1 ≠ 0, we can get: (x + 1) & # 178; > 0
So there are: 5x & # 178; + 6x-8 - (3x & # 178; + 2x-10) > 0
That is: 5x & # 178; + 6x-8 > 3x & # 178; + 2x-10