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受欢迎的代数 >

solvefor a,(a+2d)^2=a^2+(a+d)^2

解答

求解

a, (a + 2 d)^{2} = a^{2} + (a + d)^{2}

解答

a = - d, a = 3 d

求解步骤

(a + 2 d)^{2} = a^{2} + (a + d)^{2}

展开

(a + 2 d)^{2} : a^{2} + 4 a d + 4 d^{2}

展开

a^{2} + (a + d)^{2} : 2 a^{2} + 2 a d + d^{2}

a^{2} + 4 a d + 4 d^{2} = 2 a^{2} + 2 a d + d^{2}

将

d^{2}

para o lado esquerdo

a^{2} + 4 a d + 3 d^{2} = 2 a^{2} + 2 a d

将

2 a d

para o lado esquerdo

3 d^{2} + 2 a d + a^{2} = 2 a^{2}

将

2 a^{2}

para o lado esquerdo

3 d^{2} + 2 a d - a^{2} = 0

改写成标准形式

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

- a^{2} + 2 d a + 3 d^{2} = 0

使用求根公式求解

a_{1, 2} = \frac{- 2 d \pm ( 2 d ) ^{2} - 4 ( - 1 ) \cdot 3 d ^{2}}{2 ( - 1 )}

化简

(2 d)^{2} - 4 (- 1) \cdot 3 d^{2} : 4 d

a_{1, 2} = \frac{- 2 d \pm 4 d}{2 ( - 1 )}

将解分隔开

a_{1} = \frac{- 2 d + 4 d}{2 ( - 1 )}, a_{2} = \frac{- 2 d - 4 d}{2 ( - 1 )}

a = \frac{- 2 d + 4 d}{2 ( - 1 )} : - d

a = \frac{- 2 d - 4 d}{2 ( - 1 )} : 3 d

二次方程组的解是:

a = - d, a = 3 d

作图

流行的例子

completesquare 4x^2-5x-6=0

co m pl e t es q u a re 4 x^{2} - 5 x - 6 = 0

solvefor x,xy-x^2+e^y=5

so l v e f or x, x y - x^{2} + e^{y} = 5

3 x^{2} - 25 x + 8 = 0

2x^2+(6*10^{-5})x-(7.2*10^{-9})=0

2 x^{2} + (6 \cdot 1 0^{- 5}) x - (7.2 \cdot 1 0^{- 9}) = 0

solvefor A,AXB=(BA)^2

so l v e f or A, A XB = (B A)^{2}