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受欢迎的代数 >

j(2a)=(2a)^2-(2a)+1

解答

j (2 a) = (2 a)^{2} - (2 a) + 1

解答

a = \frac{1 + j + j ^{2} + 2 j - 3}{4}, a = \frac{1 + j - j ^{2} + 2 j - 3}{4}

求解步骤

j (2 a) = (2 a)^{2} - (2 a) + 1

展开

(2 a)^{2} - (2 a) + 1 : 4 a^{2} - 2 a + 1

2 ja = 4 a^{2} - 2 a + 1

交换两边

4 a^{2} - 2 a + 1 = 2 ja

将

2 ja

para o lado esquerdo

4 a^{2} - 2 a + 1 - 2 ja = 0

改写成标准形式

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

4 a^{2} - (2 + 2 j) a + 1 = 0

使用求根公式求解

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

化简

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

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

将解分隔开

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

a = \frac{- ( - 2 - 2 j ) + 2 j ^{2} + 2 j - 3}{2 \cdot 4} : \frac{1 + j + j ^{2} + 2 j - 3}{4}

a = \frac{- ( - 2 - 2 j ) - 2 j ^{2} + 2 j - 3}{2 \cdot 4} : \frac{1 + j - j ^{2} + 2 j - 3}{4}

二次方程组的解是:

a = \frac{1 + j + j ^{2} + 2 j - 3}{4}, a = \frac{1 + j - j ^{2} + 2 j - 3}{4}

作图

流行的例子

(3 x - 4)^{2} - 5 = 2

((x+x+20)x)/2 =119

\frac{( x + x + 20 ) x}{2} = 119

5 x^{2} + 60 x = - 100

3 x^{2} + 13 x - 31 = - 1

7 x^{2} - 3 = 1