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受欢迎的代数 >

((x+3)^2)/(81)-((x-4)^2)/(16)=1

解答

\frac{( x + 3 ) ^{2}}{81} - \frac{( x - 4 ) ^{2}}{16} = 1

解答

x = \frac{372}{65} - i \frac{144}{65}, x = \frac{372}{65} + i \frac{144}{65}

求解步骤

\frac{( x + 3 ) ^{2}}{81} - \frac{( x - 4 ) ^{2}}{16} = 1

找到

81, 16

的最小公倍数:

1296

乘以最小公倍数=

1296

\frac{( x + 3 ) ^{2}}{81} \cdot 1296 - \frac{( x - 4 ) ^{2}}{16} \cdot 1296 = 1 \cdot 1296

化简

16 (x + 3)^{2} - 81 (x - 4)^{2} = 1296

展开

16 (x + 3)^{2} - 81 (x - 4)^{2} : - 65 x^{2} + 744 x - 1152

- 65 x^{2} + 744 x - 1152 = 1296

将

1296

para o lado esquerdo

- 65 x^{2} + 744 x - 2448 = 0

使用求根公式求解

x_{1, 2} = \frac{- 744 \pm 74 4 ^{2} - 4 ( - 65 ) ( - 2448 )}{2 ( - 65 )}

化简

74 4^{2} - 4 (- 65) (- 2448) : 288 i

x_{1, 2} = \frac{- 744 \pm 288 i}{2 ( - 65 )}

将解分隔开

x_{1} = \frac{- 744 + 288 i}{2 ( - 65 )}, x_{2} = \frac{- 744 - 288 i}{2 ( - 65 )}

x = \frac{- 744 + 288 i}{2 ( - 65 )} : \frac{372}{65} - i \frac{144}{65}

x = \frac{- 744 - 288 i}{2 ( - 65 )} : \frac{372}{65} + i \frac{144}{65}

二次方程组的解是:

x = \frac{372}{65} - i \frac{144}{65}, x = \frac{372}{65} + i \frac{144}{65}

作图

流行的例子

3 x - 17 + 3 x^{2} = - 4

3 x^{2} - 2 = 5 x

3 x^{2} - 432 = 0

1+4+7+(3n-2)= n/2 (3n-1)

1 + 4 + 7 + (3 n - 2) = \frac{n}{2} (3 n - 1)

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