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人気のある代数 >

(3a^2+x)2=9a^4+24a^2b^2+x^2

解

(3 a^{2} + x) 2 = 9 a^{4} + 24 a^{2} b^{2} + x^{2}

解

x = 1 + - 3 a^{2} (3 a^{2} + 8 b^{2} - 2) + 1, x = 1 - - 3 a^{2} (3 a^{2} + 8 b^{2} - 2) + 1

解答ステップ

(3 a^{2} + x) \cdot 2 = 9 a^{4} + 24 a^{2} b^{2} + x^{2}

拡張

(3 a^{2} + x) \cdot 2 : 6 a^{2} + 2 x

6 a^{2} + 2 x = 9 a^{4} + 24 a^{2} b^{2} + x^{2}

辺を交換する

9 a^{4} + 24 a^{2} b^{2} + x^{2} = 6 a^{2} + 2 x

2 x

を左側に移動します

9 a^{4} + 24 a^{2} b^{2} + x^{2} - 2 x = 6 a^{2}

6 a^{2}

を左側に移動します

9 a^{4} + 24 a^{2} b^{2} + x^{2} - 2 x - 6 a^{2} = 0

標準的な形式で書く

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

x^{2} - 2 x + 9 a^{4} + 24 a^{2} b^{2} - 6 a^{2} = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( 9 a ^{4} + 24 a ^{2} b ^{2} - 6 a ^{2} )}{2 \cdot 1}

簡素化

(- 2)^{2} - 4 \cdot 1 \cdot (9 a^{4} + 24 a^{2} b^{2} - 6 a^{2}) : 2 1 - 3 a^{2} (- 2 + 3 a^{2} + 8 b^{2})

x_{1, 2} = \frac{- ( - 2 ) \pm 2 1 - 3 a ^{2} ( - 2 + 3 a ^{2} + 8 b ^{2} )}{2 \cdot 1}

解を分離する

x_{1} = \frac{- ( - 2 ) + 2 1 - 3 a ^{2} ( - 2 + 3 a ^{2} + 8 b ^{2} )}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 2 1 - 3 a ^{2} ( - 2 + 3 a ^{2} + 8 b ^{2} )}{2 \cdot 1}

x = \frac{- ( - 2 ) + 2 1 - 3 a ^{2} ( - 2 + 3 a ^{2} + 8 b ^{2} )}{2 \cdot 1} : 1 + - 3 a^{2} (3 a^{2} + 8 b^{2} - 2) + 1

x = \frac{- ( - 2 ) - 2 1 - 3 a ^{2} ( - 2 + 3 a ^{2} + 8 b ^{2} )}{2 \cdot 1} : 1 - - 3 a^{2} (3 a^{2} + 8 b^{2} - 2) + 1

二次equationの解:

x = 1 + - 3 a^{2} (3 a^{2} + 8 b^{2} - 2) + 1, x = 1 - - 3 a^{2} (3 a^{2} + 8 b^{2} - 2) + 1

グラフ

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