Question

怎样算出等于16发错了，是下面这张图

Answer 1

令x^(1/2)+x^(-1/2)=y原式化为

y(y^2-3)-2=16

y^3-3y-18=0

y^3-3y^2+3y^2-9y+6y-18=0

(y^3-3y^2)+(3y^2-9y)+(6y-18)=0

y^2(y-3)+3y(y-3)+6(y-3)=0

(y-3)(y^2+3y+6)=0

y1=3

y^2+3y+6=0

y^2+3y+(3/2)^2=9/4-6

(y+3/2)=-15/4

无实数解

x^(1/2)+x^(-1/2)=3

x+1=3x^(1/2)

x-3x^(1/2)=-1

x-3x^(1/2)+(3/2)^2=9/4-1

[x^(1/2)-3/2)^2=5/4

x^(1/2)-3/2=±√5/2

x^(1/2)=3/2±√5/2

x=(3/2±√5/2)^2

=9/4±3√5/2+5/4

=14/4±3√5/2

=7/2±3√5/2

=(7±3√5)/2