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人気のある代数 >

A(x)=x^2+pi((10-x)^2)/4

解

A (x) = x^{2} + π \frac{( 10 - x ) ^{2}}{4}

解

x = \frac{2 ( 5 π + A + - 100 π + 10 π A + A ^{2} )}{π + 4}, x = \frac{2 ( 5 π + A - - 100 π + 10 π A + A ^{2} )}{π + 4}

解答ステップ

A (x) = x^{2} + π \frac{( 10 - x ) ^{2}}{4}

拡張

x^{2} + π \frac{( 10 - x ) ^{2}}{4} : x^{2} + 25 π - 5 π x + \frac{π x ^{2}}{4}

A x = x^{2} + 25 π - 5 π x + \frac{π x ^{2}}{4}

辺を交換する

x^{2} + 25 π - 5 π x + \frac{π x ^{2}}{4} = A x

A x

を左側に移動します

x^{2} + 25 π - 5 π x + \frac{π x ^{2}}{4} - A x = 0

標準的な形式で書く

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

(\frac{π}{4} + 1) x^{2} - (5 π + A) x + 25 π = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 5 π - A ) \pm ( - 5 π - A ) ^{2} - 4 ( \frac{π}{4} + 1 ) \cdot 25 π}{2 ( \frac{π}{4} + 1 )}

簡素化

(- 5 π - A)^{2} - 4 (\frac{π}{4} + 1) \cdot 25 π : - 100 π + 10 π A + A^{2}

x_{1, 2} = \frac{- ( - 5 π - A ) \pm - 100 π + 10 π A + A ^{2}}{2 ( \frac{π}{4} + 1 )}

解を分離する

x_{1} = \frac{- ( - 5 π - A ) + - 100 π + 10 π A + A ^{2}}{2 ( \frac{π}{4} + 1 )}, x_{2} = \frac{- ( - 5 π - A ) - - 100 π + 10 π A + A ^{2}}{2 ( \frac{π}{4} + 1 )}

x = \frac{- ( - 5 π - A ) + - 100 π + 10 π A + A ^{2}}{2 ( \frac{π}{4} + 1 )} : \frac{2 ( 5 π + A + - 100 π + 10 π A + A ^{2} )}{π + 4}

x = \frac{- ( - 5 π - A ) - - 100 π + 10 π A + A ^{2}}{2 ( \frac{π}{4} + 1 )} : \frac{2 ( 5 π + A - - 100 π + 10 π A + A ^{2} )}{π + 4}

二次equationの解:

x = \frac{2 ( 5 π + A + - 100 π + 10 π A + A ^{2} )}{π + 4}, x = \frac{2 ( 5 π + A - - 100 π + 10 π A + A ^{2} )}{π + 4}

グラフ

人気の例

solvefor x,x^2y-y-x^2=0

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7 x^{2} - 7 x + 1 = 0

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z^{2} - 10 z + 34 = 0

1-7/30 x-1/15 x^2=0

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