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  • If  are the roots of the equation <img alt="7x^2 - 3x - 2 =0" src="http://entrancecorner.codecogs.com/gif.latex?7x%5E

If \alpha\ \&\ \beta are the roots of the equation 7x^2 - 3x - 2 =0 then value of \frac{\alpha}{1 - \alpha^2} + \frac{\beta}{1 - \beta^2} equals?
Option: 1 1/24  
Option: 2 3/8    
Option: 3 27/16   
Option: 4 27/32

Answers (1)

best_answer

Given quad equation 7x^2-3x-2=0 

\alpha+\beta=\frac{3}{7},\;\;\alpha\beta=-\frac{2}{7}

\\\frac{\alpha}{1-\alpha^2}+\frac{\beta}{1-\beta^2}=\frac{\alpha(1-\beta^2)+\beta(1-\alpha^2)}{(1-\alpha^2)(1-\beta^2)}\\\Rightarrow \frac{(\alpha+\beta)(1-\alpha\beta)}{1-\left [ (\alpha+\beta)^2-2\alpha\beta \right ]+(\alpha\beta)^2}\\\text{Put the value of }\alpha+\beta\;\text{and }\;\alpha\beta\\\Rightarrow \frac{27}{16}

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himanshu.meshram

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