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受欢迎的代数 >

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

解答

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

解答

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

求解步骤

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

展开

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

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

交换两边

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

将

X^{3}

para o lado esquerdo

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

使用求根公式求解

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

化简

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

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

将解分隔开

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}

二次方程组的解是:

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

作图

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