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受欢迎的代数 >

-9x^{10}+10x^9=0.75

解答

- 9 x^{10} + 10 x^{9} = 0.75

解答

x \approx 1.06304 \dots, x \approx 0.90359 \dots

求解步骤

- 9 x^{10} + 10 x^{9} = 0.75

在两边乘以

100

- 900 x^{10} + 1000 x^{9} = 75

将

75

para o lado esquerdo

- 900 x^{10} + 1000 x^{9} - 75 = 0

使用牛顿-拉弗森方法找到

- 900 x^{10} + 1000 x^{9} - 75 = 0

的一个解:

x \approx 1.06304 \dots

使用长除法

Eq u a t i o n 0 : \frac{- 900 x ^{10} + 1000 x ^{9} - 75}{x - 1.06304 \dots} = - 900 x^{9} + 43.26200 \dots x^{8} + 45.98933 \dots x^{7} + 48.88860 \dots x^{6} + 51.97065 \dots x^{5} + 55.24700 \dots x^{4} + 58.72989 \dots x^{3} + 62.43235 \dots x^{2} + 66.36823 \dots x + 70.55223 \dots

- 900 x^{9} + 43.26200 \dots x^{8} + 45.98933 \dots x^{7} + 48.88860 \dots x^{6} + 51.97065 \dots x^{5} + 55.24700 \dots x^{4} + 58.72989 \dots x^{3} + 62.43235 \dots x^{2} + 66.36823 \dots x + 70.55223 \dots \approx 0

使用牛顿-拉弗森方法找到

- 900 x^{9} + 43.26200 \dots x^{8} + 45.98933 \dots x^{7} + 48.88860 \dots x^{6} + 51.97065 \dots x^{5} + 55.24700 \dots x^{4} + 58.72989 \dots x^{3} + 62.43235 \dots x^{2} + 66.36823 \dots x + 70.55223 \dots = 0

的一个解:

x \approx 0.90359 \dots

使用长除法

Eq u a t i o n 0 : \frac{- 900 x ^{9} + 43.26200 \dots x ^{8} + 45.98933 \dots x ^{7} + 48.88860 \dots x ^{6} + 51.97065 \dots x ^{5} + 55.24700 \dots x ^{4} + 58.72989 \dots x ^{3} + 62.43235 \dots x ^{2} + 66.36823 \dots x + 70.55223 \dots}{x - 0.90359 \dots} = - 900 x^{8} - 769.97452 \dots x^{7} - 649.75667 \dots x^{6} - 538.22901 \dots x^{5} - 434.37101 \dots x^{4} - 337.24897 \dots x^{3} - 246.00697 \dots x^{2} - 159.85860 \dots x - 78.07938 \dots

- 900 x^{8} - 769.97452 \dots x^{7} - 649.75667 \dots x^{6} - 538.22901 \dots x^{5} - 434.37101 \dots x^{4} - 337.24897 \dots x^{3} - 246.00697 \dots x^{2} - 159.85860 \dots x - 78.07938 \dots \approx 0

使用牛顿-拉弗森方法找到

- 900 x^{8} - 769.97452 \dots x^{7} - 649.75667 \dots x^{6} - 538.22901 \dots x^{5} - 434.37101 \dots x^{4} - 337.24897 \dots x^{3} - 246.00697 \dots x^{2} - 159.85860 \dots x - 78.07938 \dots = 0

的一个解:

x \in R

无解

解为

x \approx 1.06304 \dots, x \approx 0.90359 \dots

作图

流行的例子

x^{7} - 81 x^{3} = 0

x^3-7x^2+8x+16=0

x^{3} - 7 x^{2} + 8 x + 16 = 0

x^{4} = \frac{1}{81}

x^3+2x^2-5x-10=0

x^{3} + 2 x^{2} - 5 x - 10 = 0

根 x^4-5x^2+4=0

roo t s x^{4} - 5 x^{2} + 4 = 0