Question

用配方法证明：2x²-x+3=0的值不小于八分之二十三

Answer 1

2x²-x+3
=2(x²-x/2)+3
=2(x²-x/2+1/16)-1/8+24/8
=2(x-1/4)²+23/8
因为(x-1/4)²>=0
所以(x-1/4)²+23/8>=23/8
即2x²-x+3=0的值不小于8分之23

Answer 2

2x²-x+3
=2(x²-x/2+3/2)
=2(x²-x/2+1/6+23/16)
=2(x-1/4)²+23/8
≥23/8
因此，
2x²-x+3的值不小于八分之二十三

Answer 3

2x²-x+3
=2(x²-x/2+1/16-1/16)+3
=2(x²-x/2+1/16)-1/8+3
=2(x-1/4)²+23/8≥23/8

Answer 4

2x²-x+3=2(x²-1/2x)+3
=2(x-1/4)²+3-1/8
=2(x-1/4)²+23/8≥23/8

题目的问法错了，不应该等于0，而是代数式不小于八分之二十三。