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人気のある代数 >

X^3=(X-300)^3+100

解

X^{3} = (X - 300)^{3} + 100

解

X = 150 - i \frac{- 27000 0 ^{2} + 97199640000}{1800}, X = 150 + i \frac{- 27000 0 ^{2} + 97199640000}{1800}

解答ステップ

X^{3} = (X - 300)^{3} + 100

拡張

(X - 300)^{3} + 100 : X^{3} - 900 X^{2} + 270000 X - 26999900

X^{3} = X^{3} - 900 X^{2} + 270000 X - 26999900

辺を交換する

X^{3} - 900 X^{2} + 270000 X - 26999900 = X^{3}

X^{3}

を左側に移動します

- 900 X^{2} + 270000 X - 26999900 = 0

解くとthe二次式

X_{1, 2} = \frac{- 270000 \pm 27000 0 ^{2} - 4 ( - 900 ) ( - 26999900 )}{2 ( - 900 )}

簡素化

27000 0^{2} - 4 (- 900) (- 26999900) : i - 27000 0^{2} + 97199640000

X_{1, 2} = \frac{- 270000 \pm i - 27000 0 ^{2} + 97199640000}{2 ( - 900 )}

解を分離する

X_{1} = \frac{- 270000 + i - 27000 0 ^{2} + 97199640000}{2 ( - 900 )}, X_{2} = \frac{- 270000 - i - 27000 0 ^{2} + 97199640000}{2 ( - 900 )}

X = \frac{- 270000 + i - 27000 0 ^{2} + 97199640000}{2 ( - 900 )} : 150 - i \frac{- 27000 0 ^{2} + 97199640000}{1800}

X = \frac{- 270000 - i - 27000 0 ^{2} + 97199640000}{2 ( - 900 )} : 150 + i \frac{- 27000 0 ^{2} + 97199640000}{1800}

二次equationの解:

X = 150 - i \frac{- 27000 0 ^{2} + 97199640000}{1800}, X = 150 + i \frac{- 27000 0 ^{2} + 97199640000}{1800}

グラフ

人気の例

b^{2} - b - 12 = 0

- n (5 n - 4) = 0

solvefor b,4^2+b^2=c^2

so l v e f or b, 4^{2} + b^{2} = c^{2}

x^{2} - 7 \cdot + 6 = 0

1.5=(4/81)(x-3)^2+1

1.5 = (\frac{4}{81}) (x - 3)^{2} + 1