((-24+2y)/(4-y))^2 = 1.225((y^2)+4y)

asked by guest
on Mar 22, 2025 at 1:16 am



You asked:

Solve the equation (−24+2y4−y)2=1.225(y2+4y){\left( \frac{-24 + 2 y}{4 - y} \right)}^{2} = 1.225 \left({y}^{2} + 4 y\right) for the variable yy.

MathBot Answer:

The complex solutions are: {1+2∣−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+619588∣−2i−619294−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+587196∣−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+619588∣,1+2∣−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+619588∣+2i−619294−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+587196∣−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+619588∣,−2−2−15120476353046+213724185432183+1670821609−15120476353046+213724185432183+619294+587196∣−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+619588∣−2∣−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+619588∣+1,−2∣−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+619588∣+1+2−2−15120476353046+213724185432183+1670821609−15120476353046+213724185432183+619294+587196∣−1670821609−15120476353046+213724185432183+2−15120476353046+213724185432183+619588∣}∖{4}\left\{1 + 2 \sqrt{\left|{- \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{619}{588}}\right|} - 2 i \sqrt{- \frac{619}{294} - \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{587}{196 \sqrt{\left|{- \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{619}{588}}\right|}}}, 1 + 2 \sqrt{\left|{- \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{619}{588}}\right|} + 2 i \sqrt{- \frac{619}{294} - \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{587}{196 \sqrt{\left|{- \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{619}{588}}\right|}}}, - 2 \sqrt{- 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + \frac{619}{294} + \frac{587}{196 \sqrt{\left|{- \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{619}{588}}\right|}}} - 2 \sqrt{\left|{- \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{619}{588}}\right|} + 1, - 2 \sqrt{\left|{- \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{619}{588}}\right|} + 1 + 2 \sqrt{- 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + \frac{619}{294} + \frac{587}{196 \sqrt{\left|{- \frac{16708}{21609 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}}} + 2 \sqrt[3]{- \frac{1512047}{6353046} + \frac{\sqrt{213724185}}{43218}} + \frac{619}{588}}\right|}}}\right\} \setminus \left\{4\right\}

ii is the imaginary unit, defined as i2=−1i^2 = -1.

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