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(5x-2)²=9(x+3)²配方法解方程
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(5x-2)²=9(x+3)²配方法解方程
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答案和解析
配方法:
(5x-2)² = 9(x+3)²
25x² - 20x + 4 = 9x² + 54x + 81
16x² - 74x = 77
x² - 37/8 x = 77/16
x² - 37/8 x + (37/16)² = 77/16 + (37/16)²
(x - 37/16)² = 2601 / 16²
x - 37/16 = ± 51/16
x₁ = 11/2 ,x₂ = - 7/8
这道题用直接开方法比较简单
(5x-2)² = 9(x+3)²
5x-2 = 3(x+3) 或 5x-2 = - 3(x+3)
x₁ = 11/2 ,x₂ = - 7/8
(5x-2)² = 9(x+3)²
25x² - 20x + 4 = 9x² + 54x + 81
16x² - 74x = 77
x² - 37/8 x = 77/16
x² - 37/8 x + (37/16)² = 77/16 + (37/16)²
(x - 37/16)² = 2601 / 16²
x - 37/16 = ± 51/16
x₁ = 11/2 ,x₂ = - 7/8
这道题用直接开方法比较简单
(5x-2)² = 9(x+3)²
5x-2 = 3(x+3) 或 5x-2 = - 3(x+3)
x₁ = 11/2 ,x₂ = - 7/8
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