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受欢迎的代数 >

x^2=2022+sqrt(2022+x)

解答

x^{2} = 2022 + 2022 + x

解答

x \approx 45.46943 \dots, x \approx - 45.45831 \dots

求解步骤

x^{2} = 2022 + 2022 + x

去除平方根

x^{4} - 4044 x^{2} + 4088484 = 2022 + x

解

x^{4} - 4044 x^{2} + 4088484 = 2022 + x : x \approx 45.46943 \dots, x \approx - 44.46943 \dots, x \approx 44.45831 \dots, x \approx - 45.45831 \dots

x \approx 45.46943 \dots, x \approx - 44.46943 \dots, x \approx 44.45831 \dots, x \approx - 45.45831 \dots

验证解:

x \approx 45.46943 \dots

真

, x \approx - 44.46943 \dots

假

, x \approx 44.45831 \dots

假

, x \approx - 45.45831 \dots

真

解为

x \approx 45.46943 \dots, x \approx - 45.45831 \dots

作图

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