x的平方减9分之x的平方减6x＋9除以二分之x－3,其中x等于根号2－3

Question

如题所述

Answer 1

x的平方减9分之x的平方减6x＋9除以二分之x－3,其中x等于根号2－3
x²-x²/9-6x+9÷x/2-3
=8x²/9-6x-3+9(2/x)
=8x²/9-6x-3+18/x
用x=√2-3代入
=8(√2-3)²/9-6(√2-3)-3+18/(√2-3)
=8(2-6√2+9)/9-6(√2-3)-3+18(√2+3)/[(√2-3)(√2+3)]
=8(11-6√2)/9-6(√2-3)-3+18(√2+3)/(2-9)
=(88-48√2)/9-6√2+18-3+18(√2+3)/(-7)
=(88-48√2)/9-6√2+15-(18√2+54)/7
=(88-48√2)/9-(18√2+54)/7-6√2+15
=7(88-48√2)/63-9(18√2+54)/63-6√2+15
=(616-336√2)/63-(162√2+486)/63-6√2+15
=(616-336√2-162√2-486)/63-6√2+15
=(616-486-336√2-162√2)/63-6√2+15
=(130-498√2)/63-6√2+15
=(130-498√2)/63-378√2/63+945/63
=(1084-876√2)/63