解方程式 (16x 27)^2(8x 15)..

Question

解方程式 (16x  27)2(8x  15)(2x 3) = 7

(16x + 27)2(8x + 15)(2x + 3) = 7

Answer 1

(16x + 27)²(8x + 15)(2x + 3) = 7
(16x + 27)²(16x ²+ 54x + 45) = 7
(16x + 27)²[(4x + 27/4)² - 9/16] = 7
(16x + 27)²(4x + 27/4)² - 9/16(16x + 27)² = 7
兩邊同×16
(16x + 27)²(16x + 27)² - 9(16x + 27)² = 112

令 A = (16x + 27)²
原式
A² - 9A - 112 = 0
A=16 , -7

<實數根>
16x + 27 = ±4
x= －23/16 , －31/16

<複數根>
16x + 27 = ±√7i
x = (－27 ±√ 7i)／16

Answer 2

(16x + 27)^2*(8x + 15)*(2x + 3) = 7 乘開後變成4096*x^4+14848*x^3+15040*x^2+3096*x+180=7==>4096*x^4+14848*x^3+15040*x^2+3096*x+173=0這是一元四次方程式我利用計算機程式MATLAB解>> p=[4096,14848,15040,3096,173];>> roots(p)ans =   -1.8765   -1.4976   -0.1521   -0.0988得到4個解-----------------------------------乘開我也是用程式解的>> clear>> syms x>> f=(16*x+2)^2 f = (16*x+2)^2  >> a=expand(f) a = 256*x^2+64*x+4>> a*(8*x+15)*(2*x+3) ans = (256*x^2+64*x+4)*(8*x+15)*(2*x+3) >> expand(ans) ans = 4096*x^4+14848*x^3+15040*x^2+3096*x+180 >> ans-7 ans = 4096*x^4+14848*x^3+15040*x^2+3096*x+173