Question

如果x平方减2x减1等于0，3x的4次方加5x的3次方减7x平方加5的值

Answer 1

x²-2x-1=0,
x²=2x+1
x=1±√2

3x^4+5x³-7x²+5
=x²(3x²+5x-7)+5
=(2x+1)(6x+3+5x-7)+5
=(2x+1)(11x-4)+5
=22x²+3x+1
=44x+22+3x+1
=47x+23
当x=1+√2时，原式=70+47√2
当x=1-√2时，原式=70-47√2

Answer 2

x²-2x-1=0,
x²=2x+1 兼（x-1）²=2
x=1±√2

3x^4+5x³-7x²+5
=（x-1）²（3x²+11x+12）+13x-7
=6x²+35x+17
=6（x-1）²+47x+11
=47x+23
当x=1+√2时，原式=70+47√2
当x=1-√2时，原式=70-47√2