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人気のある代数 >

solvefor a,f(a^2)=f^{-1}(a+2)

解

解く

a, f (a^{2}) = f^{- 1} (a + 2)

解

a = \frac{1 + 1 + 8 f ^{2}}{2 f ^{2}}, a = \frac{1 - 1 + 8 f ^{2}}{2 f ^{2}}; f \neq = 0

解答ステップ

f (a^{2}) = f^{- 1} (a + 2)

拡張

f^{- 1} (a + 2) : \frac{a}{f} + \frac{2}{f}

a^{2} f = \frac{a}{f} + \frac{2}{f}

両辺から

\frac{a}{f} + \frac{2}{f}

を引く

a^{2} f - (\frac{a}{f} + \frac{2}{f}) = \frac{a}{f} + \frac{2}{f} - (\frac{a}{f} + \frac{2}{f})

簡素化

f a^{2} - \frac{a}{f} - \frac{2}{f} = 0

解くとthe二次式

a_{1, 2} = \frac{- ( - \frac{1}{f} ) \pm ( - \frac{1}{f} ) ^{2} - 4 f ( - \frac{2}{f} )}{2 f}

簡素化

(- \frac{1}{f})^{2} - 4 f (- \frac{2}{f}) : \frac{1 + 8 f ^{2}}{f}

a_{1, 2} = \frac{- ( - \frac{1}{f} ) \pm \frac{1 + 8 f ^{2}}{f}}{2 f}; f \neq = 0

解を分離する

a_{1} = \frac{- ( - \frac{1}{f} ) + \frac{1 + 8 f ^{2}}{f}}{2 f}, a_{2} = \frac{- ( - \frac{1}{f} ) - \frac{1 + 8 f ^{2}}{f}}{2 f}

a = \frac{- ( - \frac{1}{f} ) + \frac{1 + 8 f ^{2}}{f}}{2 f} : \frac{1 + 1 + 8 f ^{2}}{2 f ^{2}}

a = \frac{- ( - \frac{1}{f} ) - \frac{1 + 8 f ^{2}}{f}}{2 f} : \frac{1 - 1 + 8 f ^{2}}{2 f ^{2}}

二次equationの解:

a = \frac{1 + 1 + 8 f ^{2}}{2 f ^{2}}, a = \frac{1 - 1 + 8 f ^{2}}{2 f ^{2}}; f \neq = 0

グラフ

人気の例

X^{2} + 5 X - 6 = 0

802.2=0.68*2.14*100*x*(9.5-0.4*x)

802.2 = 0.68 \cdot 2.14 \cdot 100 \cdot x \cdot (9.5 - 0.4 \cdot x)

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

因数 2x^2-5x=3

f a c t or 2 x^{2} - 5 x = 3

x^{2} + 2 x + 1 = 3