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人気のある代数 >

solvefor b,a(a+b)(a+b+c)=11

解

解く

b, a (a + b) (a + b + c) = 11

解

b = \frac{- 2 a ^{2} - a c + a ^{2} c ^{2} + 44 a}{2 a}, b = \frac{- 2 a ^{2} - a c - a ^{2} c ^{2} + 44 a}{2 a}; a \neq = 0

解答ステップ

a (a + b) (a + b + c) = 11

拡張

a (a + b) (a + b + c) : 2 b a^{2} + a^{2} c + a^{3} + b^{2} a + ba c

2 b a^{2} + a^{2} c + a^{3} + b^{2} a + ba c = 11

11

を左側に移動します

2 b a^{2} + a^{2} c + a^{3} + b^{2} a + ba c - 11 = 0

標準的な形式で書く

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

a b^{2} + (2 a^{2} + a c) b + a^{2} c + a^{3} - 11 = 0

解くとthe二次式

b_{1, 2} = \frac{- ( 2 a ^{2} + a c ) \pm ( 2 a ^{2} + a c ) ^{2} - 4 a ( a ^{2} c + a ^{3} - 11 )}{2 a}

簡素化

(2 a^{2} + a c)^{2} - 4 a (a^{2} c + a^{3} - 11) : a^{2} c^{2} + 44 a

b_{1, 2} = \frac{- ( 2 a ^{2} + a c ) \pm a ^{2} c ^{2} + 44 a}{2 a}; a \neq = 0

解を分離する

b_{1} = \frac{- ( 2 a ^{2} + a c ) + a ^{2} c ^{2} + 44 a}{2 a}, b_{2} = \frac{- ( 2 a ^{2} + a c ) - a ^{2} c ^{2} + 44 a}{2 a}

b = \frac{- ( 2 a ^{2} + a c ) + a ^{2} c ^{2} + 44 a}{2 a} : \frac{- 2 a ^{2} - a c + a ^{2} c ^{2} + 44 a}{2 a}

b = \frac{- ( 2 a ^{2} + a c ) - a ^{2} c ^{2} + 44 a}{2 a} : \frac{- 2 a ^{2} - a c - a ^{2} c ^{2} + 44 a}{2 a}

二次equationの解:

b = \frac{- 2 a ^{2} - a c + a ^{2} c ^{2} + 44 a}{2 a}, b = \frac{- 2 a ^{2} - a c - a ^{2} c ^{2} + 44 a}{2 a}; a \neq = 0

グラフ

人気の例

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