Question

已知（x²-3x+1）分之x=1,求（x⁴-9x²+1）分之x²的值

Answer 1

（x²-3x+1）分之x=1

x分之（x²-3x+1）=1

x-3+1/x=1

x+1/x=4

所以

（x⁴-9x²+1）分之x²

=（x²-9+1/x²）分之1

=【(x+1/x)²-11】分之1

=【16-11】分之1

=5分之1