-9x^{1/2}+x^{3/2}=16

解答

- 9 x^{\frac{1}{2}} + x^{\frac{3}{2}} = 16

x \approx 13.37495 \dots

求解步骤

- 9 x^{\frac{1}{2}} + x^{\frac{3}{2}} = 16

因式分解

- 9 x^{\frac{1}{2}} + x^{\frac{3}{2}} : x^{\frac{1}{2}} (- 9 + x)

x^{\frac{1}{2}} (- 9 + x) = 16

两边进行平方:

81 x - 18 x^{2} + x^{3} = 256

81 x - 18 x^{2} + x^{3} = 256

解

81 x - 18 x^{2} + x^{3} = 256 : x \approx 13.37495 \dots

x \approx 13.37495 \dots

验证解:

x \approx 13.37495 \dots

真

解是

x \approx 13.37495 \dots

e x t re m e f (x) = x^{2} + 2 x + 2

in v erse f (x) = (x - 7)^{\frac{1}{3}}

r an g e f (x) = - x^{2} - 6 x + 1

p a r i t y y = \frac{x}{x ^{3} - x + 5}

in v erse f (x) = \frac{- 4 x + 4}{x - 5}