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人気のある代数 >

(n+1)(x^2+2x)=(n+3)(3x+5)

解

(n + 1) (x^{2} + 2 x) = (n + 3) (3 x + 5)

解

x = \frac{n + 7 + 21 n ^{2} + 94 n + 109}{2 ( n + 1 )}, x = \frac{n + 7 - 21 n ^{2} + 94 n + 109}{2 ( n + 1 )}; n \neq = - 1

解答ステップ

(n + 1) (x^{2} + 2 x) = (n + 3) (3 x + 5)

拡張

(n + 1) (x^{2} + 2 x) : n x^{2} + 2 n x + x^{2} + 2 x

拡張

(n + 3) (3 x + 5) : 3 n x + 5 n + 9 x + 15

n x^{2} + 2 n x + x^{2} + 2 x = 3 n x + 5 n + 9 x + 15

15

を左側に移動します

n x^{2} + 2 n x + x^{2} + 2 x - 15 = 3 n x + 5 n + 9 x

9 x

を左側に移動します

n x^{2} + x^{2} + 2 n x - 7 x - 15 = 3 n x + 5 n

両辺から

3 n x + 5 n

を引く

n x^{2} + x^{2} + 2 n x - 7 x - 15 - (3 n x + 5 n) = 3 n x + 5 n - (3 n x + 5 n)

簡素化

(n + 1) x^{2} - (n + 7) x - 5 n - 15 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - n - 7 ) \pm ( - n - 7 ) ^{2} - 4 ( n + 1 ) ( - 5 n - 15 )}{2 ( n + 1 )}

簡素化

(- n - 7)^{2} - 4 (n + 1) (- 5 n - 15) : 21 n^{2} + 94 n + 109

x_{1, 2} = \frac{- ( - n - 7 ) \pm 21 n ^{2} + 94 n + 109}{2 ( n + 1 )}; n \neq = - 1

解を分離する

x_{1} = \frac{- ( - n - 7 ) + 21 n ^{2} + 94 n + 109}{2 ( n + 1 )}, x_{2} = \frac{- ( - n - 7 ) - 21 n ^{2} + 94 n + 109}{2 ( n + 1 )}

x = \frac{- ( - n - 7 ) + 21 n ^{2} + 94 n + 109}{2 ( n + 1 )} : \frac{n + 7 + 21 n ^{2} + 94 n + 109}{2 ( n + 1 )}

x = \frac{- ( - n - 7 ) - 21 n ^{2} + 94 n + 109}{2 ( n + 1 )} : \frac{n + 7 - 21 n ^{2} + 94 n + 109}{2 ( n + 1 )}

二次equationの解:

x = \frac{n + 7 + 21 n ^{2} + 94 n + 109}{2 ( n + 1 )}, x = \frac{n + 7 - 21 n ^{2} + 94 n + 109}{2 ( n + 1 )}; n \neq = - 1

グラフ

人気の例

x^{2} - 19 x + 84 = 0

completesquare x^2+2/3 x+5

co m pl e t es q u a re x^{2} + \frac{2}{3} x + 5

2 x^{2} - 5 = - 3 x

completesquare 5x^2-10x+3

co m pl e t es q u a re 5 x^{2} - 10 x + 3

x^{2} - 5 = - 4