当a满足条件__时,不等式a>=2根号a-1成立

问题描述:

当a满足条件__时,不等式a>=2根号a-1成立

1)(a²)^6÷a^8+(-2a)²×(1/2a²)
=a^12÷a^8+4a²*1/2a²
=a^4+2a^4
=3a^4
(2)(-2x)³×(-xy²)²+(x³y²)²÷x
=-8x³*(x²y^4)+(x^6y^4)÷y
=-8x^5y^4+x^6y³
(3)a²×(-2a²)²÷a³-2a³
=a²*(4a^4)÷a³-2a³
=4a^(2+4-3)-2a³
=4a³-2a³
=2a³

根号下大于等于0
所以a-1>=0
a>=1
a>=2√(a-1)>=0
两边平方
a²>=4a-4
a²-4a+4>=0
(a-2)²>=0
恒成立
所以a>=1