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受欢迎的代数 >

2(a+5)x^2-(a+5)x+1=0

解答

2 (a + 5) \cdot x^{2} - (a + 5) \cdot x + 1 = 0

解答

x = \frac{a + 5 + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}, x = \frac{a + 5 - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}; a \neq = - 5

求解步骤

2 (a + 5) x^{2} - (a + 5) x + 1 = 0

展开

2 (a + 5) x^{2} - (a + 5) x + 1 : 2 a x^{2} + 10 x^{2} - a x - 5 x + 1

2 a x^{2} + 10 x^{2} - a x - 5 x + 1 = 0

改写成标准形式

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

(2 a + 10) x^{2} - (a + 5) x + 1 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - a - 5 ) \pm ( - a - 5 ) ^{2} - 4 ( 2 a + 10 ) \cdot 1}{2 ( 2 a + 10 )}

化简

(- a - 5)^{2} - 4 (2 a + 10) \cdot 1 : a^{2} + 2 a - 15

x_{1, 2} = \frac{- ( - a - 5 ) \pm a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}; a \neq = - 5

将解分隔开

x_{1} = \frac{- ( - a - 5 ) + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}, x_{2} = \frac{- ( - a - 5 ) - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}

x = \frac{- ( - a - 5 ) + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )} : \frac{a + 5 + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}

x = \frac{- ( - a - 5 ) - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )} : \frac{a + 5 - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}

二次方程组的解是:

x = \frac{a + 5 + a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}, x = \frac{a + 5 - a ^{2} + 2 a - 15}{2 ( 2 a + 10 )}; a \neq = - 5

作图

流行的例子

solvefor a,(1+a+b)^2=3(a^2+b^2+1)

so l v e f or a, (1 + a + b)^{2} = 3 (a^{2} + b^{2} + 1)

(x-2)^2=(3x+2)^2

(x - 2)^{2} = (3 x + 2)^{2}

solvefor x,(x^2)/((a)^2)+(y^2)/((b)^2)=0

so l v e f or x, \frac{x ^{2}}{( a ) ^{2}} + \frac{y ^{2}}{( b ) ^{2}} = 0

solvefor x,-(x-1)^2+(y-1)^2=0

so l v e f or x, - (x - 1)^{2} + (y - 1)^{2} = 0

2 (y^{2} - 11) = 0