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受欢迎的 Geometry >

solvefor x,2^2=h(x)^2+(x/2)^2

解答

求解

x, 2^{2} = h (x)^{2} + (\frac{x}{2})^{2}

解答

x = \frac{4}{4 h + 1}, x = - \frac{4}{4 h + 1}; h \neq = - \frac{1}{4}

求解步骤

2^{2} = h x^{2} + (\frac{x}{2})^{2}

展开

2^{2} : 4

展开

h x^{2} + (\frac{x}{2})^{2} : x^{2} h + \frac{x ^{2}}{4}

4 = x^{2} h + \frac{x ^{2}}{4}

交换两边

x^{2} h + \frac{x ^{2}}{4} = 4

将

4

para o lado esquerdo

x^{2} h + \frac{x ^{2}}{4} - 4 = 0

改写成标准形式

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

(h + \frac{1}{4}) x^{2} - 4 = 0

使用求根公式求解

x_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 ( h + \frac{1}{4} ) ( - 4 )}{2 ( h + \frac{1}{4} )}

化简

0^{2} - 4 (h + \frac{1}{4}) (- 4) : 2 4 h + 1

x_{1, 2} = \frac{- 0 \pm 2 4 h + 1}{2 ( h + \frac{1}{4} )}; h \neq = - \frac{1}{4}

将解分隔开

x_{1} = \frac{- 0 + 2 4 h + 1}{2 ( h + \frac{1}{4} )}, x_{2} = \frac{- 0 - 2 4 h + 1}{2 ( h + \frac{1}{4} )}

x = \frac{- 0 + 2 4 h + 1}{2 ( h + \frac{1}{4} )} : \frac{4}{4 h + 1}

x = \frac{- 0 - 2 4 h + 1}{2 ( h + \frac{1}{4} )} : - \frac{4}{4 h + 1}

二次方程组的解是:

x = \frac{4}{4 h + 1}, x = - \frac{4}{4 h + 1}; h \neq = - \frac{1}{4}

作图

流行的例子

4 x^{2} + y^{2} \leq 17

((x+8)^2)/(20)+((y+36)^2)/(36)=1

\frac{( x + 8 ) ^{2}}{20} + \frac{( y + 36 ) ^{2}}{36} = 1

4x^2+y^2-16x-2y+1=0

4 x^{2} + y^{2} - 16 x - 2 y + 1 = 0

5 x^{2} + z^{2} = 100

(25x^2)/(400-12^2)+(16y^2)/(400-12^2)=1

\frac{25 x ^{2}}{400 - 1 2 ^{2}} + \frac{16 y ^{2}}{400 - 1 2 ^{2}} = 1