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受欢迎的代数 >

9(sqrt(4x+1)-sqrt(3x-2))=x+3

解答

9 (4 x + 1 - 3 x - 2) = x + 3

解答

x = 6

求解步骤

9 (4 x + 1 - 3 x - 2) = x + 3

展开

9 (4 x + 1 - 3 x - 2) : 9 4 x + 1 - 9 3 x - 2

9 4 x + 1 - 9 3 x - 2 = x + 3

去除平方根

972 x^{3} + 5184 x^{2} + 4860 x - 5832 = x^{4} - 150 x^{3} + 5157 x^{2} + 35100 x + 54756

交换两边

x^{2} + 18 x 3 x - 2 + 249 x + 54 3 x - 2 - 153 = 324 x + 81

将

x^{2}

到右边

18 x 3 x - 2 + 249 x + 54 3 x - 2 - 153 = 324 x + 81 - x^{2}

将

249 x

到右边

18 x 3 x - 2 + 54 3 x - 2 - 153 = - x^{2} + 75 x + 81

将

153

到右边

18 x 3 x - 2 + 54 3 x - 2 = - x^{2} + 75 x + 234

分解

18 x 3 x - 2 + 54 3 x - 2 : 18 3 x - 2 (x + 3)

18 3 x - 2 (x + 3) = - x^{2} + 75 x + 234

解

972 x^{3} + 5184 x^{2} + 4860 x - 5832 = x^{4} - 150 x^{3} + 5157 x^{2} + 35100 x + 54756 : x = - 3, x = 6, x = 1122

x = - 3, x = 6, x = 1122

验证解:

x = - 3

假

, x = 6

真

, x = 1122

假

解是

x = 6

作图

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