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受欢迎的代数 >

xsqrt(x)+sqrt(x-\sqrt{x)}=2x

解答

x x + x - x = 2 x

解答

x = 0, x \approx 2.61803 \dots

求解步骤

x x + x - x = 2 x

去除平方根

x - 8 x^{3} + 16 x^{5} = 8 x^{5} + x^{6} + 14 x^{4} - 8 x^{3} + x^{2}

将

x

到右边

- x = 4 x^{2} - 4 x x^{2} + x^{3} - x

将

4 x x^{2}

para o lado esquerdo

- x + 4 x x^{2} = 4 x^{2} + x^{3} - x

分解

- x + 4 x x^{2} : x (- 1 + 4 x^{2})

x (- 1 + 4 x^{2}) = 4 x^{2} + x^{3} - x

解

x - 8 x^{3} + 16 x^{5} = 8 x^{5} + x^{6} + 14 x^{4} - 8 x^{3} + x^{2} : x = 0, x \approx 0.38196 \dots, x \approx 2.61803 \dots, x \approx 5.40431 \dots

x = 0, x \approx 0.38196 \dots, x \approx 2.61803 \dots, x \approx 5.40431 \dots

验证解:

x = 0

真

, x \approx 0.38196 \dots

假

, x \approx 2.61803 \dots

真

, x \approx 5.40431 \dots

假

解为

x = 0, x \approx 2.61803 \dots

作图

流行的例子

b = - x - 4 x

(x+28)^{1/3}-(x-28)^{1/3}=2

(x + 28)^{\frac{1}{3}} - (x - 28)^{\frac{1}{3}} = 2

x^{2} = 3

x^{2} = 7

solvefor r,x^2(r^2-x^2)^{0.5}=1

so l v e f or r, x^{2} (r^{2} - x^{2})^{0.5} = 1