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4-2.Quadratic Equations and Inequations
normal
જો $\alpha $, $\beta$, $\gamma$ એ સમીકરણ ${x^3} - 2{x^2} + 3x - 2 = 0$ ના બીજો હોય તો $\left( {\frac{{\alpha \beta }}{{\alpha + \beta }} + \frac{{\alpha \gamma }}{{\alpha + \gamma }} + \frac{{\beta \gamma }}{{\beta + \gamma }}} \right)$ ની કિમત મેળવો
A
$\frac{{13}}{4}$
B
$\frac{{25}}{18}$
C
$\frac{{9}}{2}$
D
એક પણ નહી
Solution
$x^{3}-2 x^{2}+3 x-2=(x-1)\left(x^{2}-x+2\right)$
$\alpha=1, \beta+\gamma=1, \beta \gamma=2$
$\frac{\alpha \beta}{\alpha+\beta}+\frac{\alpha \gamma}{\alpha+\gamma}+\frac{\beta \gamma}{\beta+\gamma}=\frac{\beta}{1+\beta}+\frac{\gamma}{1+\gamma}+2$
$=\frac{5}{4}+2=\frac{13}{4}$
Standard 11
Mathematics
