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受欢迎的代数 >

5(m+n-1)x^2+4(m-n)x+(mn)/(12)=0

解答

5 (m + n - 1) x^{2} + 4 (m - n) x + \frac{mn}{12} = 0

解答

x = \frac{- 48 m + 48 n + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}, x = \frac{- 48 m + 48 n - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}; 60 m + 60 n - 60 \neq = 0

求解步骤

5 (m + n - 1) x^{2} + 4 (m - n) x + \frac{mn}{12} = 0

在两边乘以

12

60 x^{2} (m + n - 1) + 48 x (m - n) + mn = 0

展开

60 x^{2} (m + n - 1) + 48 x (m - n) + mn : 60 m x^{2} + 60 n x^{2} - 60 x^{2} + 48 m x - 48 n x + mn

60 m x^{2} + 60 n x^{2} - 60 x^{2} + 48 m x - 48 n x + mn = 0

改写成标准形式

a x^{2} + b x + c = 0

(60 m + 60 n - 60) x^{2} + (48 m - 48 n) x + mn = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 48 m - 48 n ) \pm ( 48 m - 48 n ) ^{2} - 4 ( 60 m + 60 n - 60 ) mn}{2 ( 60 m + 60 n - 60 )}

化简

(48 m - 48 n)^{2} - 4 (60 m + 60 n - 60) mn : - 240 m^{2} n + 2304 m^{2} - 240 m n^{2} - 4368 mn + 2304 n^{2}

x_{1, 2} = \frac{- ( 48 m - 48 n ) \pm - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}; 60 m + 60 n - 60 \neq = 0

将解分隔开

x_{1} = \frac{- ( 48 m - 48 n ) + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}, x_{2} = \frac{- ( 48 m - 48 n ) - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}

x = \frac{- ( 48 m - 48 n ) + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )} : \frac{- 48 m + 48 n + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}

x = \frac{- ( 48 m - 48 n ) - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )} : \frac{- 48 m + 48 n - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}

二次方程组的解是:

x = \frac{- 48 m + 48 n + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}, x = \frac{- 48 m + 48 n - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}; 60 m + 60 n - 60 \neq = 0

作图

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