Question

在线等高一的指数与指数幂的运算1.已知a^x=根号2+1 求 (a^2x)-(a^-2x)/(a^x) + (a^-x)

Answer 1

1.

(a^2x)-(a^-2x)/(a^x) + (a^-x)

=((a^x)-(a^-x)）（(a^x)+(a^-x)）/(a^x) + (a^-x)

=(a^x) - (a^-x)

=√2+1-(√2-1)

=2

2.

x>0,y>0否则式子无意义

x-y=((x+y)^2-4xy)^1/2

=6√3

(x^1/2)-(y^1/2) /(x^1/2)+(y^1/2)

=((x^1/2)-(y^1/2))((x^1/2)+(y^1/2)) / (x^1/2)+(y^1/2) ((x^1/2)+(y^1/2) )

=(x-y)/(x+y+2(xy)^1/2)

=6√3/(12+2*3)

=√3/3

3.

a = 2 - √3

b = 2 + √3

a+b=4

ab=1

aa+bb=14

(a+1)^-2 + (b+1)^-2

=(aa+bb+2(a+b)+2)/((ab+a+b+1)^2)

=(14+8+2)/(1+4+1)^2

=2/3