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人気のある代数 >

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

解

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

解

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

解答ステップ

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

以下で両辺を乗じる:

12

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

拡張

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

標準的な形式で書く

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

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

解くとthe二次式

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 )}

簡素化

(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

解を分離する

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equationの解:

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

グラフ

人気の例

9 w^{2} - 27 w + 20 = 0

- x^{2} + 2 x = 2

- x (- 6 (x) + 1) = 1

solvefor y,2x^2-xy+y^2=16

so l v e f or y, 2 x^{2} - x y + y^{2} = 16

x^2+2/3 x-1/9 =0

x^{2} + \frac{2}{3} x - \frac{1}{9} = 0