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受欢迎的代数 >

((X+3)^2}{16}-\frac{(X-7)^2)/4 =1

解答

\frac{( X + 3 ) ^{2}}{16} - \frac{( X - 7 ) ^{2}}{4} = 1

解答

X = \frac{31 - 4 22}{3}, X = \frac{31 + 4 22}{3}

+1

十进制

X = 4.07944 \dots, X = 16.58722 \dots

求解步骤

\frac{( X + 3 ) ^{2}}{16} - \frac{( X - 7 ) ^{2}}{4} = 1

找到

16, 4

的最小公倍数:

16

乘以最小公倍数=

16

\frac{( X + 3 ) ^{2}}{16} \cdot 16 - \frac{( X - 7 ) ^{2}}{4} \cdot 16 = 1 \cdot 16

化简

(X + 3)^{2} - 4 (X - 7)^{2} = 16

展开

(X + 3)^{2} - 4 (X - 7)^{2} : - 3 X^{2} + 62 X - 187

- 3 X^{2} + 62 X - 187 = 16

将

16

para o lado esquerdo

- 3 X^{2} + 62 X - 203 = 0

使用求根公式求解

X_{1, 2} = \frac{- 62 \pm 6 2 ^{2} - 4 ( - 3 ) ( - 203 )}{2 ( - 3 )}

6 2^{2} - 4 (- 3) (- 203) = 822

X_{1, 2} = \frac{- 62 \pm 8 22}{2 ( - 3 )}

将解分隔开

X_{1} = \frac{- 62 + 8 22}{2 ( - 3 )}, X_{2} = \frac{- 62 - 8 22}{2 ( - 3 )}

X = \frac{- 62 + 8 22}{2 ( - 3 )} : \frac{31 - 4 22}{3}

X = \frac{- 62 - 8 22}{2 ( - 3 )} : \frac{31 + 4 22}{3}

二次方程组的解是:

X = \frac{31 - 4 22}{3}, X = \frac{31 + 4 22}{3}

作图

流行的例子

2 x^{2} + 32 x + 272 = 0

2 x^{2} - 12 x + 26 = 0

completesquare x^2+6x+8

co m pl e t es q u a re x^{2} + 6 x + 8

v^{2} = 25

m^{2} + 4 m + 3 = 0