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受欢迎的代数 >

(x+5)(2-x)=3sqrt(x^2+x)

解答

(x + 5) (2 - x) = 3 x^{2} + x

解答

x \approx 1.21001 \dots, x \approx - 3.41025 \dots

求解步骤

(x + 5) (2 - x) = 3 x^{2} + x

展开

(x + 5) (2 - x) : - 3 x - x^{2} + 10

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

两边进行平方:

6 x^{3} + x^{4} - 11 x^{2} - 60 x + 100 = 9 x^{2} + 9 x

6 x^{3} + x^{4} - 11 x^{2} - 60 x + 100 = 9 x^{2} + 9 x

解

6 x^{3} + x^{4} - 11 x^{2} - 60 x + 100 = 9 x^{2} + 9 x : x \approx 1.21001 \dots, x \approx - 3.41025 \dots, x \approx 3.37681 \dots, x \approx - 7.17657 \dots

x \approx 1.21001 \dots, x \approx - 3.41025 \dots, x \approx 3.37681 \dots, x \approx - 7.17657 \dots

验证解:

x \approx 1.21001 \dots

真

, x \approx - 3.41025 \dots

真

, x \approx 3.37681 \dots

假

, x \approx - 7.17657 \dots

假

解为

x \approx 1.21001 \dots, x \approx - 3.41025 \dots

作图

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