Question

已知y^2+3y-1=0,求y^4/y^8-3y^4+1的值

Answer 1

∵y²+3y-1=0,

∴y-1/y=-3

(y-1/y)²=(-3)²

y²-2+1/y²=9

y²+1/y²=11

同理：y^4+1/y^4=119

(y^8-3y^4+1)/y^4 把原式反过来.

=y^4+1/y^4-3

=119-3

=116

所以y^4/(y^8-3y^4+1)=1/116