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受欢迎的代数 >

(ax^2+3bx+8)+(2x^2-4x+c)=5x^2-2x+3

解答

(a x^{2} + 3 b x + 8) + (2 x^{2} - 4 x + c) = 5 x^{2} - 2 x + 3

解答

x = \frac{- 3 b + 2 + - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )}, x = \frac{- 3 b + 2 - - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )}; a \neq = 3

求解步骤

(a x^{2} + 3 b x + 8) + (2 x^{2} - 4 x + c) = 5 x^{2} - 2 x + 3

整理后得

a x^{2} + 3 b x + 8 + 2 x^{2} - 4 x + c = 5 x^{2} - 2 x + 3

将

3

para o lado esquerdo

a x^{2} + 2 x^{2} + 3 b x - 4 x + c + 5 = 5 x^{2} - 2 x

将

2 x

para o lado esquerdo

a x^{2} + 2 x^{2} + 3 b x - 2 x + c + 5 = 5 x^{2}

将

5 x^{2}

para o lado esquerdo

a x^{2} - 3 x^{2} + 3 b x - 2 x + c + 5 = 0

改写成标准形式

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

(a - 3) x^{2} + (3 b - 2) x + c + 5 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 3 b - 2 ) \pm ( 3 b - 2 ) ^{2} - 4 ( a - 3 ) ( c + 5 )}{2 ( a - 3 )}

化简

(3 b - 2)^{2} - 4 (a - 3) (c + 5) : - 4 a c - 20 a + 9 b^{2} + 12 c + 64 - 12 b

x_{1, 2} = \frac{- ( 3 b - 2 ) \pm - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )}; a \neq = 3

将解分隔开

x_{1} = \frac{- ( 3 b - 2 ) + - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )}, x_{2} = \frac{- ( 3 b - 2 ) - - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )}

x = \frac{- ( 3 b - 2 ) + - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )} : \frac{- 3 b + 2 + - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )}

x = \frac{- ( 3 b - 2 ) - - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )} : \frac{- 3 b + 2 - - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )}

二次方程组的解是:

x = \frac{- 3 b + 2 + - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )}, x = \frac{- 3 b + 2 - - 4 a c - 20 a + 9 b ^{2} + 12 c + 64 - 12 b}{2 ( a - 3 )}; a \neq = 3

作图

流行的例子

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y^{2} - 5 y - 84 = 0

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