已知√2≈1.414,√3≈1.732,求√12-√1⼀27+2√32的近似值

√12-√1/27+2√32
=2√3-1/9√3+8√2
=17/9√3+8√2
=17/9×1.732+8×1.414
=3.272+11.312
=14.584

(1)3x(x-1)=2-2x
3x²-3x-2+2x=0
3x²-x-2=0
(3x+2)(x-1)=0
3x+2=0 x-1=0
∴x1=-2/3
x2=1

(2)[8(x^2+2x)]/x^2-1+[3(x^2-1)]/x^2+2x=11
8(x²+2x)²+3(x²-1)²-11(x²+2x)(x²-1)=0
[(x²+2x)-(x²-1)][8(x²+2x)-3(x²-1)]=0
(2x+1)((5x²+16x+3)=0
(2x+1)(5x+1)(x+3)=0
∴2x+1=0 5x+1=0 x+3=0
∴x1=-1/2
x2=-1/5
x3=-3

根号12=2根号3
根号（1/27)=（根号3）/9
2根号32=8根号2
∴原式=（17根号3）/9+8根号2
≈14.584

√12-√1/27+2√32
=2√3-(√3)/9+8√2
≈2*1.732-1.732/9+8*1.414
≈14.968