求解(数学题)

来源:百度知道 编辑:UC知道 时间:2024/06/08 22:44:07
已知a2-a-1=0,且(2a4-3xa2+2)/(a3+2xa2-a)=-93/112,则x的值为是多少

要详细过程

x = 5.1

a^2 - a - 1 = 0
a^2 - 1 = a, a^2 = a + 1
a^3 - a = a^2

(2a^4 - 3xa^2 + 2)/(a^3 + 2xa^2 - a) = -93/112
(2a^4 - 3xa^2 + 2)/[(1 + 2x)a^2] = -93/112
-93[(1 + 2x)a^2] = 112(2a^4 - 3xa^2 + 2)
-93(1 + 2x)a^2 = 224a^4 - 336xa^2 + 224
224a^4 + [93(1 + 2x) - 336x]a^2 + 224 = 0
224a^4 + [93 - 150x]a^2 + 224 = 0
224(a+1)^2 + [93 - 150x](a+1) + 224 = 0

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

224(3a+2) + [93 - 150x](a+1) + 224 = 0
3*224(a+1) + [93 - 150x](a+1) = 0
224(a+1) + [31 - 50x](a+1) = 0
(a+1)[224 + 31 - 50x] = 0
(a+1)[255 - 50x] = 0
(a+1)[51 - 10x] = 0
x = 5.1

a^2-a-1=0
a^2=a+1
a^3=a^2+a
a^4=(a+1)^2=a^2+2a+1=3a+2
(2a4-3xa2+2)/(a3+2xa2-a)=-93/112,
(6a+4+3a^2x+2)/(a^2+a+2a^2x-a)=-93/112
(6a+6+3a^2x)/(a^2+2a^2x)=-93/112
(6a^2+3a^2x)/(a^2+2a^2x)=-93/112
a^2(6+3x)/a^2(1+2x)=-93/112
(6+3x)/(1+2x)=-93/112
112(6+3