1. **Problem statement:** Given the equation $$\frac{ب = م (2 - س ) - (7 - 4)}{3} = 1 = \frac{م}{6 - س - س^2} 2$$ and asked to find the value of $م$. 2. **Rewrite the equation clearly:** $$\frac{م (2 - س) - (7 - 4)}{3} = 1 = \frac{م}{6 - س - س^2} 2$$ 3. **Focus on the first equality:** $$\frac{م (2 - س) - 3}{3} = 1$$ 4. **Multiply both sides by 3 to clear the denominator:** $$م (2 - س) - 3 = 3$$ 5. **Add 3 to both sides:** $$م (2 - س) = 6$$ 6. **Solve for $م$:** $$م = \frac{6}{2 - س}$$ 7. **Now consider the second equality:** $$1 = \frac{م}{6 - س - س^2} 2$$ 8. **Rewrite the right side:** $$1 = \frac{2م}{6 - س - س^2}$$ 9. **Multiply both sides by denominator:** $$6 - س - س^2 = 2م$$ 10. **Substitute $م$ from step 6:** $$6 - س - س^2 = 2 \times \frac{6}{2 - س} = \frac{12}{2 - س}$$ 11. **Multiply both sides by $(2 - س)$:** $$(6 - س - س^2)(2 - س) = 12$$ 12. **Expand the left side:** $$6 \times 2 - 6 \times س - 6 \times س^2 - س \times 2 + س^2 + س^3 = 12$$ $$12 - 6س - 6س^2 - 2س + س^2 + س^3 = 12$$ 13. **Combine like terms:** $$12 - 8س - 5س^2 + س^3 = 12$$ 14. **Subtract 12 from both sides:** $$-8س - 5س^2 + س^3 = 0$$ 15. **Rewrite:** $$س^3 - 5س^2 - 8س = 0$$ 16. **Factor out $س$:** $$س (س^2 - 5س - 8) = 0$$ 17. **Set each factor to zero:** - $س = 0$ - $س^2 - 5س - 8 = 0$ 18. **Solve quadratic:** $$س = \frac{5 \pm \sqrt{25 + 32}}{2} = \frac{5 \pm \sqrt{57}}{2}$$ 19. **Possible values of $س$ are:** $$0, \frac{5 + \sqrt{57}}{2}, \frac{5 - \sqrt{57}}{2}$$ 20. **Calculate $م$ for each $س$ using step 6:** - For $س=0$: $$م = \frac{6}{2 - 0} = 3$$ - For $س=\frac{5 + \sqrt{57}}{2}$: $$م = \frac{6}{2 - \frac{5 + \sqrt{57}}{2}} = \frac{6}{\frac{4 - 5 - \sqrt{57}}{2}} = \frac{6}{\frac{-1 - \sqrt{57}}{2}} = \frac{6 \times 2}{-1 - \sqrt{57}} = \frac{12}{-1 - \sqrt{57}}$$ - For $س=\frac{5 - \sqrt{57}}{2}$: $$م = \frac{6}{2 - \frac{5 - \sqrt{57}}{2}} = \frac{6}{\frac{4 - 5 + \sqrt{57}}{2}} = \frac{6}{\frac{-1 + \sqrt{57}}{2}} = \frac{12}{-1 + \sqrt{57}}$$ 21. **Final answer:** The value of $م$ depends on $س$ and can be: $$م = 3$$ or $$م = \frac{12}{-1 - \sqrt{57}}$$ or $$م = \frac{12}{-1 + \sqrt{57}}$$