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受欢迎的代数 >

65Q-(Q^2)/(100)-(722+(Q^2)/(200))=0

解答

65 Q - \frac{Q ^{2}}{100} - (722 + \frac{Q ^{2}}{200}) = 0

解答

Q = \frac{6500 - 20 104542}{3}, Q = \frac{6500 + 20 104542}{3}

+1

十进制

Q = 11.13631 \dots, Q = 4322.19702 \dots

求解步骤

65 Q - \frac{Q ^{2}}{100} - (722 + \frac{Q ^{2}}{200}) = 0

在两边乘以

100

6500 Q - Q^{2} - 100 (722 + \frac{Q ^{2}}{200}) = 0

展开

6500 Q - Q^{2} - 100 (722 + \frac{Q ^{2}}{200}) : - \frac{3 Q ^{2}}{2} + 6500 Q - 72200

- \frac{3 Q ^{2}}{2} + 6500 Q - 72200 = 0

使用求根公式求解

Q_{1, 2} = \frac{- 6500 \pm 650 0 ^{2} - 4 ( - \frac{3}{2} ) ( - 72200 )}{2 ( - \frac{3}{2} )}

650 0^{2} - 4 (- \frac{3}{2}) (- 72200) = 20104542

Q_{1, 2} = \frac{- 6500 \pm 20 104542}{2 ( - \frac{3}{2} )}

将解分隔开

Q_{1} = \frac{- 6500 + 20 104542}{2 ( - \frac{3}{2} )}, Q_{2} = \frac{- 6500 - 20 104542}{2 ( - \frac{3}{2} )}

Q = \frac{- 6500 + 20 104542}{2 ( - \frac{3}{2} )} : \frac{6500 - 20 104542}{3}

Q = \frac{- 6500 - 20 104542}{2 ( - \frac{3}{2} )} : \frac{6500 + 20 104542}{3}

二次方程组的解是:

Q = \frac{6500 - 20 104542}{3}, Q = \frac{6500 + 20 104542}{3}

作图

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