Y的平方+3Y-1=0y+3-1/y=0y-1/y=-3(y-1/y)^2=9y^2+1/y^2-2=9y^2+1/y^2=11(y^2+1/y^2)=121y^4+1/y^4+y^2+1/y^2-2=9y^2+1/y^2=11那个-2是怎么来的?

Question

Y的平方+3Y-1=0 y+3-1/y=0 y-1/y=-3 (y-1/y)^2=9 y^2+1/y^2-2=9 y^2+1/y^2=11 (y^2+1/y^2)=121 y^4+1/y^4+
y^2+1/y^2-2=9
y^2+1/y^2=11
那个-2是怎么来的?

Answer 1

(a-b)^2=a^2-2ab+b^2
所以 （y-1/y)^2
=y^2-2*y*1/y+1/y^2
=y^2-2+1/y^2