1,
2x²-6x+7
=2(x²-3x+9/4-9/4)+7
=2(x-3/2)²-9/2+7
=2(x-3/2)²+7-9/2
2(x-3/2)²>=0,7-9/2=5/2,
2x²-6x+7>=5/2,
2x²-6x+7>0;
2,
2x²+x-3
=2(x²+x/2+1/16-1/16)-3
=2(x+1/4)²-1/8-3
=2(x+1/4)²-25/8
x=-1/4時,代數(shù)式有最小值-25/8,故代數(shù)式的值>=-25/8,因此代數(shù)式2X的平方+X-3的值不小于-25/8.