1.已知a+b+c=4,ab+bc+ac=4,求a²+b²+c².2.已知aˆ2x=√2+1,求aˆ3x+aˆ-3x/aˆx+aˆ-x.3.已知x+y=12,xy=27,且x＜y.求xˆ½-yˆ½除以xˆ½+yˆ½.

Question

1.已知a+b+c=4,ab+bc+ac=4,求a²+b²+c².2.已知aˆ2x=√2+1,求aˆ3x+aˆ-3x/aˆx+aˆ-x.3.已知x+y=12,xy=27,且x＜y.求xˆ½-yˆ½除以xˆ½+yˆ½.

Answer 1

1),a²+b²+c²=(a+b+c)²-2(ab+bc+ac)=16-8=8
2),aˆ3x+aˆ-3x=(aˆx+aˆ-x)(aˆ2x+aˆ-2x -1)
aˆ3x+aˆ-3x/aˆx+aˆ-x=aˆ2x+aˆ-2x -1=√2+1+√2-1 - 1=2√2 -1
3)第三题~是负号吗?x+y=12,xy=27,(y-x)²=(y+x)²-4xy=144-108=36,所以y-x=6
xˆ½-yˆ½除以xˆ½+yˆ½=(1/√x - 1/√y)/(1/√x +1/√y) =(√y-√x )/(√y+√x )= ( y+x-2√xy)/(y-x)=（12-2√27）/6
=2-√3