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人気のある代数 >

solvefor p,(y-px)^2=1+p^2

解

解く

p, (y - p x)^{2} = 1 + p^{2}

解

p = \frac{y x + y ^{2} + x ^{2} - 1}{x ^{2} - 1}, p = \frac{y x - y ^{2} + x ^{2} - 1}{x ^{2} - 1}; x \neq = 1, x \neq = - 1

解答ステップ

(y - p x)^{2} = 1 + p^{2}

拡張

(y - p x)^{2} : y^{2} - 2 p y x + p^{2} x^{2}

y^{2} - 2 p y x + p^{2} x^{2} = 1 + p^{2}

p^{2}

を左側に移動します

y^{2} - 2 p y x + p^{2} x^{2} - p^{2} = 1

1

を左側に移動します

y^{2} - 2 p y x + p^{2} x^{2} - p^{2} - 1 = 0

標準的な形式で書く

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

(x^{2} - 1) p^{2} - 2 y x p + y^{2} - 1 = 0

解くとthe二次式

p_{1, 2} = \frac{- ( - 2 y x ) \pm ( - 2 y x ) ^{2} - 4 ( x ^{2} - 1 ) ( y ^{2} - 1 )}{2 ( x ^{2} - 1 )}

簡素化

(- 2 y x)^{2} - 4 (x^{2} - 1) (y^{2} - 1) : 2 x^{2} + y^{2} - 1

p_{1, 2} = \frac{- ( - 2 y x ) \pm 2 x ^{2} + y ^{2} - 1}{2 ( x ^{2} - 1 )}; x \neq = 1, x \neq = - 1

解を分離する

p_{1} = \frac{- ( - 2 y x ) + 2 x ^{2} + y ^{2} - 1}{2 ( x ^{2} - 1 )}, p_{2} = \frac{- ( - 2 y x ) - 2 x ^{2} + y ^{2} - 1}{2 ( x ^{2} - 1 )}

p = \frac{- ( - 2 y x ) + 2 x ^{2} + y ^{2} - 1}{2 ( x ^{2} - 1 )} : \frac{y x + y ^{2} + x ^{2} - 1}{x ^{2} - 1}

p = \frac{- ( - 2 y x ) - 2 x ^{2} + y ^{2} - 1}{2 ( x ^{2} - 1 )} : \frac{y x - y ^{2} + x ^{2} - 1}{x ^{2} - 1}

二次equationの解:

p = \frac{y x + y ^{2} + x ^{2} - 1}{x ^{2} - 1}, p = \frac{y x - y ^{2} + x ^{2} - 1}{x ^{2} - 1}; x \neq = 1, x \neq = - 1

グラフ

人気の例

solvefor x,A=(x+y)(x+y)

so l v e f or x, A = (x + y) (x + y)

solvefor x,x^2+y^2-4x-2y+7=0

so l v e f or x, x^{2} + y^{2} - 4 x - 2 y + 7 = 0

a^{2} - 10 a + 21 = 0

1 5^{2} + 1 2^{2} = c^{2}

(X + 3)^{2} - 13 = - 4