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受欢迎的代数 >

1/(sqrt(1-x^2))= pi/2

解答

\frac{1}{1 - x ^{2}} = \frac{π}{2}

解答

x = \frac{- 4 + π ^{2}}{π}, x = - \frac{- 4 + π ^{2}}{π}

+1

十进制

x = 0.77117 \dots, x = - 0.77117 \dots

求解步骤

\frac{1}{1 - x ^{2}} = \frac{π}{2}

使用分式交叉相乘: 若

\frac{a}{b} = \frac{c}{d}

则

a \cdot d = b \cdot c

1 \cdot 2 = 1 - x^{2} π

交换两边

1 - x^{2} π = 1 \cdot 2

数字相乘:

1 \cdot 2 = 2

1 - x^{2} π = 2

两边除以

π

1 - x^{2} = \frac{2}{π}

两边进行平方:

1 - x^{2} = \frac{4}{π ^{2}}

1 - x^{2} = \frac{4}{π ^{2}}

解

1 - x^{2} = \frac{4}{π ^{2}} : x = \frac{- 4 + π ^{2}}{π}, x = - \frac{- 4 + π ^{2}}{π}

x = \frac{- 4 + π ^{2}}{π}, x = - \frac{- 4 + π ^{2}}{π}

验证解:

x = \frac{- 4 + π ^{2}}{π}

真

, x = - \frac{- 4 + π ^{2}}{π}

真

解为

x = \frac{- 4 + π ^{2}}{π}, x = - \frac{- 4 + π ^{2}}{π}

作图

流行的例子

sqrt(x+5)+sqrt(x-2)=sqrt(5x-6)

x + 5 + x - 2 = 5 x - 6

-x+(3x-11)^{1/2}=-3

- x + (3 x - 11)^{\frac{1}{2}} = - 3

x^{1/2}-7x^{1/4}+12=0

x^{\frac{1}{2}} - 7 x^{\frac{1}{4}} + 12 = 0

1-1/3 x^{-2/3}=0

1 - \frac{1}{3} x^{- \frac{2}{3}} = 0

solvefor y,5sqrt(xy)-2sqrt(y)-3sqrt(x)=0

so l v e f or y, 5 x y - 2 y - 3 x = 0