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受欢迎的代数 >

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

解答

求解

a, (1 + a + b)^{2} = 3 (a^{2} + b^{2} + 1)

解答

a = \frac{1 + b}{2} + i \frac{3 - 3 b}{2}, a = \frac{1 + b}{2} + i \frac{- 3 + 3 b}{2}

求解步骤

(1 + a + b)^{2} = 3 (a^{2} + b^{2} + 1)

展开

(1 + a + b)^{2} : 2 ab + 2 b + b^{2} + 2 a + a^{2} + 1

展开

3 (a^{2} + b^{2} + 1) : 3 a^{2} + 3 b^{2} + 3

2 ab + 2 b + b^{2} + 2 a + a^{2} + 1 = 3 a^{2} + 3 b^{2} + 3

将

3

para o lado esquerdo

b^{2} + 2 ab + 2 b + a^{2} + 2 a - 2 = 3 a^{2} + 3 b^{2}

将

3 b^{2}

para o lado esquerdo

- 2 b^{2} + 2 ab + 2 b + a^{2} + 2 a - 2 = 3 a^{2}

将

3 a^{2}

para o lado esquerdo

- 2 a^{2} + 2 ab + 2 a - 2 b^{2} + 2 b - 2 = 0

改写成标准形式

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

- 2 a^{2} + (2 b + 2) a - 2 b^{2} + 2 b - 2 = 0

使用求根公式求解

a_{1, 2} = \frac{- ( 2 b + 2 ) \pm ( 2 b + 2 ) ^{2} - 4 ( - 2 ) ( - 2 b ^{2} + 2 b - 2 )}{2 ( - 2 )}

化简

(2 b + 2)^{2} - 4 (- 2) (- 2 b^{2} + 2 b - 2) : i (- 23 + 23 b)

a_{1, 2} = \frac{- ( 2 b + 2 ) \pm i ( - 2 3 + 2 3 b )}{2 ( - 2 )}

将解分隔开

a_{1} = \frac{- ( 2 b + 2 ) + i ( - 2 3 + 2 3 b )}{2 ( - 2 )}, a_{2} = \frac{- ( 2 b + 2 ) - i ( - 2 3 + 2 3 b )}{2 ( - 2 )}

a = \frac{- ( 2 b + 2 ) + i ( - 2 3 + 2 3 b )}{2 ( - 2 )} : \frac{1 + b}{2} + i \frac{3 - 3 b}{2}

a = \frac{- ( 2 b + 2 ) - i ( - 2 3 + 2 3 b )}{2 ( - 2 )} : \frac{1 + b}{2} + i \frac{- 3 + 3 b}{2}

二次方程组的解是:

a = \frac{1 + b}{2} + i \frac{3 - 3 b}{2}, a = \frac{1 + b}{2} + i \frac{- 3 + 3 b}{2}

作图

流行的例子

(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

(t)=576+64t-t^2

(t) = 576 + 64 t - t^{2}