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受欢迎的代数 >

N(a)=-2a^2+150a+3,0<= a<= 400

解答

N (a) = - 2 a^{2} + 150 a + 3, 0 \leq a \leq 400

解答

a = - \frac{- 150 + N + N ^{2} - 300 N + 22524}{4}, a = - \frac{- 150 + N - N ^{2} - 300 N + 22524}{4}

求解步骤

N (a) = - 2 a^{2} + 150 a + 3

整理后得

N a = - 2 a^{2} + 150 a + 3

交换两边

- 2 a^{2} + 150 a + 3 = N a

将

N a

para o lado esquerdo

- 2 a^{2} + 150 a + 3 - N a = 0

改写成标准形式

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

- 2 a^{2} + (150 - N) a + 3 = 0

使用求根公式求解

a_{1, 2} = \frac{- ( 150 - N ) \pm ( 150 - N ) ^{2} - 4 ( - 2 ) \cdot 3}{2 ( - 2 )}

化简

(150 - N)^{2} - 4 (- 2) \cdot 3 : N^{2} - 300 N + 22524

a_{1, 2} = \frac{- ( 150 - N ) \pm N ^{2} - 300 N + 22524}{2 ( - 2 )}

将解分隔开

a_{1} = \frac{- ( 150 - N ) + N ^{2} - 300 N + 22524}{2 ( - 2 )}, a_{2} = \frac{- ( 150 - N ) - N ^{2} - 300 N + 22524}{2 ( - 2 )}

a = \frac{- ( 150 - N ) + N ^{2} - 300 N + 22524}{2 ( - 2 )} : - \frac{- 150 + N + N ^{2} - 300 N + 22524}{4}

a = \frac{- ( 150 - N ) - N ^{2} - 300 N + 22524}{2 ( - 2 )} : - \frac{- 150 + N - N ^{2} - 300 N + 22524}{4}

二次方程组的解是:

a = - \frac{- 150 + N + N ^{2} - 300 N + 22524}{4}, a = - \frac{- 150 + N - N ^{2} - 300 N + 22524}{4}

作图

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