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受欢迎的代数 >

4x^2+15x^9=0

解答

4 x^{2} + 15 x^{9} = 0

解答

x = 0, x = - 7 \frac{4}{15}

+1

十进制

x = 0, x = - 0.82793 \dots

求解步骤

4 x^{2} + 15 x^{9} = 0

因式分解

4 x^{2} + 15 x^{9} : x^{2} (715 x + 74) (1 5^{\frac{6}{7}} x^{6} - 74 \cdot 1 5^{\frac{5}{7}} x^{5} + 4^{\frac{2}{7}} \cdot 1 5^{\frac{4}{7}} x^{4} - 6 0^{\frac{3}{7}} x^{3} + 4^{\frac{4}{7}} \cdot 1 5^{\frac{2}{7}} x^{2} - 4^{\frac{5}{7}} 715 x + 4^{\frac{6}{7}})

x^{2} (715 x + 74) (1 5^{\frac{6}{7}} x^{6} - 74 \cdot 1 5^{\frac{5}{7}} x^{5} + 4^{\frac{2}{7}} \cdot 1 5^{\frac{4}{7}} x^{4} - 6 0^{\frac{3}{7}} x^{3} + 4^{\frac{4}{7}} \cdot 1 5^{\frac{2}{7}} x^{2} - 4^{\frac{5}{7}} 715 x + 4^{\frac{6}{7}}) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or 715 x + 74 = 0 or 1 5^{\frac{6}{7}} x^{6} - 74 \cdot 1 5^{\frac{5}{7}} x^{5} + 4^{\frac{2}{7}} \cdot 1 5^{\frac{4}{7}} x^{4} - 6 0^{\frac{3}{7}} x^{3} + 4^{\frac{4}{7}} \cdot 1 5^{\frac{2}{7}} x^{2} - 4^{\frac{5}{7}} 715 x + 4^{\frac{6}{7}} = 0

解

715 x + 74 = 0 : x = - 7 \frac{4}{15}

解

1 5^{\frac{6}{7}} x^{6} - 74 \cdot 1 5^{\frac{5}{7}} x^{5} + 4^{\frac{2}{7}} \cdot 1 5^{\frac{4}{7}} x^{4} - 6 0^{\frac{3}{7}} x^{3} + 4^{\frac{4}{7}} \cdot 1 5^{\frac{2}{7}} x^{2} - 4^{\frac{5}{7}} 715 x + 4^{\frac{6}{7}} = 0 : x \in R

无解

解为

x = 0, x = - 7 \frac{4}{15}

作图

流行的例子

-((x^4))/(10)+14/15*x^3-2x^2=0

- \frac{( x ^{4} )}{10} + \frac{14}{15} \cdot x^{3} - 2 x^{2} = 0

x^{2} (x^{2} - 9) = - 20

(x - 1)^{3} = x - 1

2 (x - 2)^{3} + 8 = 136

x^3-11x^2+32x-28=0

x^{3} - 11 x^{2} + 32 x - 28 = 0