Question

已知a^2-a-1=0且(2a^4-3xa^2+2)/(a^3+2xa^2-2)= - 93/112求x的值

Answer 1

a^2-a-1=0
a^2-1=a
a-1/a=1
a^2+1/a^2=(a-1/a)^2+2=3

a^3-2
=a^3-2(a^2-a)
=a^3+2a-2a^2
=a(a^2+2)-2a^2
=(a^2-1)(a^2+2)-2a^2
=a^4-a^2+1

(2a^4-3xa^2+2)/(a^3+2xa^2-2)=-93/112
(2a^4-3a^2x+2)/(a^4-a^2+1+2a^2x)=-93/112
224a^4-336a^2x+224=-93a^4+93a^2-93-186a^2x
317a^4-93a^2+317=150a^2x
x=317/150(a^2+1/a^2)-93/150
x=317*3/150-93/150
x=143/25

真的很难做 加点分吧...

Answer 2

a^2-a-1=0，==> a-(1/a)=1, a^2+(1/a^2)=3
(2a^4-3xa^2+2)/(a^3+2xa^2-a)=-93/112
左边分子分母同时除以a^2,得
[2a^2-3x+(2/a^2)]/[a+2x-(1/a)]=-93/112
既：
(6-3x)/(1+2x)=-93/112
解得：
x=10/51

Answer 3

解：由题意可得a2-a-1=0
a2=a+1
a4=（a2）2=（a+1）2=a2+2a+1=a+1+2a+1=3a+2
a3=a•a2=a（a+1）=a2+a=a+1+a=2a+1
2a4-3a2x+2 a3+2a2x-a =-93 1126a+4-3a2x+2 2a+1+2a2x-a =-93 112
672a+672-336xa2=-93a-93-186xa2
150xa2=765a+765=765（a+1）=765a2
150x=765
x=5.1．

Answer 4

a^2=a+1带入即可解

Answer 5

都没有看到X,是求a吧

Answer 6

x=5.1