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受欢迎的代数 >

((x-3)^2}{16}-\frac{(x-4)^2)/9 =1

解答

\frac{( x - 3 ) ^{2}}{16} - \frac{( x - 4 ) ^{2}}{9} = 1

解答

x = \frac{37}{7} - i \frac{12 6}{7}, x = \frac{37}{7} + i \frac{12 6}{7}

求解步骤

\frac{( x - 3 ) ^{2}}{16} - \frac{( x - 4 ) ^{2}}{9} = 1

找到

16, 9

的最小公倍数:

144

乘以最小公倍数=

144

\frac{( x - 3 ) ^{2}}{16} \cdot 144 - \frac{( x - 4 ) ^{2}}{9} \cdot 144 = 1 \cdot 144

化简

9 (x - 3)^{2} - 16 (x - 4)^{2} = 144

展开

9 (x - 3)^{2} - 16 (x - 4)^{2} : - 7 x^{2} + 74 x - 175

- 7 x^{2} + 74 x - 175 = 144

将

144

para o lado esquerdo

- 7 x^{2} + 74 x - 319 = 0

使用求根公式求解

x_{1, 2} = \frac{- 74 \pm 7 4 ^{2} - 4 ( - 7 ) ( - 319 )}{2 ( - 7 )}

化简

7 4^{2} - 4 (- 7) (- 319) : 246 i

x_{1, 2} = \frac{- 74 \pm 24 6 i}{2 ( - 7 )}

将解分隔开

x_{1} = \frac{- 74 + 24 6 i}{2 ( - 7 )}, x_{2} = \frac{- 74 - 24 6 i}{2 ( - 7 )}

x = \frac{- 74 + 24 6 i}{2 ( - 7 )} : \frac{37}{7} - i \frac{12 6}{7}

x = \frac{- 74 - 24 6 i}{2 ( - 7 )} : \frac{37}{7} + i \frac{12 6}{7}

二次方程组的解是:

x = \frac{37}{7} - i \frac{12 6}{7}, x = \frac{37}{7} + i \frac{12 6}{7}

作图

流行的例子

a^{2} + 2 = 2 a

solvefor x,4x^2y^2+2xy-12=0

so l v e f or x, 4 x^{2} y^{2} + 2 x y - 12 = 0

(x+4)^2-(2x+3)(x-2)=42

(x + 4)^{2} - (2 x + 3) (x - 2) = 42

6(x+1)-(4-x)(x+1)=6(4-x)

6 (x + 1) - (4 - x) (x + 1) = 6 (4 - x)

solvefor y,4x^3-2x=2y^2+7

so l v e f or y, 4 x^{3} - 2 x = 2 y^{2} + 7