Question

已知3加根号2和3减根号2的小数部分分别为a，b，求ab-3a+4b-7的值

Answer 1

a=3+√2 - 4=√2-1
b=3-√2 -1=2-√2
ab - 3a + 4b -7
=(√2-1)(2-√2) - 3(√2-1) + 4(2-√2) -7
=3√3 - 4 -3√2 +3 +8 -4√2 -7
=-4√2

Answer 2

a= 小数部分(3+√2)= √2 -1
b= 小数部分(3-√2) = 2-√2

ab-3a+4b-7
=(√2 -1)( 2-√2) -3(√2 -1) +4( 2-√2) -7
=-4+3√2 -3(√2 -1) +4( 2-√2) -7
=(-4+3+8-7) +(3-3-4)√2
=-4√2

Answer 3

根号2约等于1.414,
3+根号2约等于4.414,大于4,则a=3+根号2-4=根号2-1,
3-根号2约等于1.586,大于1,则b=3-根号2-1=2-根号2,
ab=(根号2-1)*(2-根号2)=3根号2-4,
-3a=-3(根号2-1)=3-3根号2,
4b=4(2-根号2)=8-4根号2,
ab-3a+4b-7
=3根号2-4+3-3根号2+8-4根号2-7
=-4根号2