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受欢迎的代数 >

10=u^{0.5}+u^{0.8}+u^{1.1}

解答

10 = u^{0.5} + u^{0.8} + u^{1.1}

解答

u = 4.17653 \dots

求解步骤

10 = u^{0.5} + u^{0.8} + u^{1.1}

使用以下的指数特性

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

u^{0.8} = (u^{\frac{1}{2}})^{(0.8 \cdot 2)}, u^{1.1} = (u^{\frac{1}{2}})^{(1.1 \cdot 2)}

10 = u^{\frac{1}{2}} + (u^{\frac{1}{2}})^{\frac{8}{5}} + (u^{\frac{1}{2}})^{\frac{11}{5}}

用

u^{\frac{1}{2}} = v

改写方程式

10 = v + v^{\frac{8}{5}} + v^{\frac{11}{5}}

解

10 = v + v^{\frac{8}{5}} + v^{\frac{11}{5}} : v = 2.04365 \dots

v = 2.04365 \dots

代回

v = u^{\frac{1}{2}}

，求解

u

解

u^{\frac{1}{2}} = 2.04365 \dots : u = 4.17653 \dots

u = 4.17653 \dots

验证解:

u = 4.17653 \dots

真

解是

u = 4.17653 \dots

作图

流行的例子

(x-1)^{3/2}+15=7

(x - 1)^{\frac{3}{2}} + 15 = 7

3 x - 8 = 2

3 x - 8 = 7

x^{2} + 11 = 6

sqrt(1^2+1^2+x^2)=1

1^{2} + 1^{2} + x^{2} = 1