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受欢迎的代数 >

g(n)=n^2+3,g(8)

解答

g (n) = n^{2} + 3, g (8)

解答

n = \frac{g + g ^{2} - 12}{2}, n = \frac{g - g ^{2} - 12}{2}

求解步骤

g (n) = n^{2} + 3

整理后得

g n = n^{2} + 3

交换两边

n^{2} + 3 = g n

将

g n

para o lado esquerdo

n^{2} + 3 - g n = 0

改写成标准形式

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

n^{2} - g n + 3 = 0

使用求根公式求解

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

化简

(- g)^{2} - 4 \cdot 1 \cdot 3 : g^{2} - 12

n_{1, 2} = \frac{- ( - g ) \pm g ^{2} - 12}{2 \cdot 1}

将解分隔开

n_{1} = \frac{- ( - g ) + g ^{2} - 12}{2 \cdot 1}, n_{2} = \frac{- ( - g ) - g ^{2} - 12}{2 \cdot 1}

n = \frac{- ( - g ) + g ^{2} - 12}{2 \cdot 1} : \frac{g + g ^{2} - 12}{2}

n = \frac{- ( - g ) - g ^{2} - 12}{2 \cdot 1} : \frac{g - g ^{2} - 12}{2}

二次方程组的解是:

n = \frac{g + g ^{2} - 12}{2}, n = \frac{g - g ^{2} - 12}{2}

作图

流行的例子

4 x^{2} - 8 x - 23 = 0

x^{2} + 4 x - 117 = 0

0 = 3 x^{2} - 24 x + 45

8 x^{2} - 5 = 195

5 x^{2} + 3 = x^{2} - 7