If-x-3y-6z-7z-2-and-y-1-2-z-6y-3-2-z-6y-Find-x-3-y-3-

Question Number 9009 by tawakalitu last updated on 13/Nov/16

If : x = \frac{3 y + 6 z}{7 z - 2} and y = \frac{\frac{1}{2} z + 6 y}{\frac{3}{2} z + 6 y}

Find : x^{3} + y^{3}

Answered by Rasheed Soomro last updated on 14/Nov/16

If : x = \frac{3 y + 6 z}{7 z - 2} and y = \frac{\frac{1}{2} z + 6 y}{\frac{3}{2} z + 6 y} = \frac{z + 12 y}{3 z + 12 y}

y = \frac{z + 12 y}{3 z + 12 y} \Rightarrow 3 yz + {12 y}^{2} = z + 12 y

{12 y}^{2} + 3 (z - 4) y - z = 0

y = \frac{- 3 (z - 4) \pm \sqrt{9 {(z - 4)}^{2} + 48 z}}{24}

= \frac{- 3 (z - 4) \pm \sqrt{{9 z}^{2} - 24 z + 144}}{24}

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x = \frac{3 y + 6 z}{7 z - 2} = \frac{3 (\frac{- 3 (z - 4) \pm \sqrt{{9 z}^{2} - 24 z + 144}}{24}) + 6 z}{7 z - 2}

= \frac{\frac{- 3 (z - 4) \pm \sqrt{{9 z}^{2} - 24 z + 144}}{8} + 6 z}{7 z - 2}

= \frac{\frac{- 3 (z - 4) \pm \sqrt{{9 z}^{2} - 24 z + 144} + 48 z}{8}}{7 z - 2}

= \frac{45 z + 12 \pm \sqrt{{9 z}^{2} - 24 z + 144}}{8 (7 z - 2)}

x^{3} + y^{3} = {(\frac{45 z + 12 \pm \sqrt{{9 z}^{2} - 24 z + 144}}{8 (7 z - 2)})}^{3} + {(\frac{- 3 (z - 4) \pm \sqrt{{9 z}^{2} - 24 z + 144}}{24})}^{3}

Commented by tawakalitu last updated on 13/Nov/16

thanks sir . will be expecting .

Commented by tawakalitu last updated on 14/Nov/16

i really appreciate sir . God bless you .