Subjects algebra

Algebra Expressions 009983

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1. Berilgan ifoda: $$\frac{\left(\frac{1}{a} + \frac{1}{b} - \frac{c}{ab}\right)(a + b + c)}{\frac{1}{a^2} + \frac{1}{b^2} + \frac{2}{5}ab - \frac{c^2}{a^2b^2}}$$ 2. Qiymatlarni qo'yamiz: $a=10.4$, $b=\frac{5}{26}$, $c=0.124$ 3. Yuqoridagi ifodani hisoblaymiz: $$\frac{\left(\frac{1}{10.4} + \frac{1}{\frac{5}{26}} - \frac{0.124}{10.4 \cdot \frac{5}{26}}\right)(10.4 + \frac{5}{26} + 0.124)}{\frac{1}{(10.4)^2} + \frac{1}{\left(\frac{5}{26}\right)^2} + \frac{2}{5} \cdot 10.4 \cdot \frac{5}{26} - \frac{(0.124)^2}{(10.4)^2 \cdot \left(\frac{5}{26}\right)^2}}$$ 4. Hisoblash: $$\frac{\left(0.0961538 + 5.2 - 0.0061538\right)(10.4 + 0.192308 + 0.124)}{0.009247 + 27.04 + 4.16 - 0.000142} = \frac{(5.29)(10.7163)}{31.209} = \frac{56.67}{31.209} \approx 1.815$$ 5. Ikkinchi ifoda: $$\left(\frac{1}{a^2} + \frac{1}{b^2} + \frac{2}{ab} - \frac{c^2}{a^2b^2}\right) \text{ ifodaning qiymatini } \left(\frac{c}{ab} - \frac{1}{a} - \frac{1}{b}\right)(a + b + c)$$ 6. Qiymatlar: $a=2.4$, $b=\frac{5}{6}$, $c$ berilmagan, shuning uchun hisoblash mumkin emas. 7. Uchinchi ifoda: $$\frac{b + c}{a} + \frac{a + c}{b} + \frac{a + b}{c}$$ 8. Shartlar: $a + b + c = 8$, $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{3}{2}$ 9. Hisoblash: $$\frac{b+c}{a} + \frac{a+c}{b} + \frac{a+b}{c} = \left(\frac{a+b+c}{a} - 1\right) + \left(\frac{a+b+c}{b} - 1\right) + \left(\frac{a+b+c}{c} - 1\right) = (8)(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) - 3 = 8 \times \frac{3}{2} - 3 = 12 - 3 = 9$$