Exams Joint Entrance Examination Mathematics Quadratic Equations and Inequalities Question 124 Question 124 of 157 Medium MCQ
If \[\alpha \] and \[\beta \] are the roots of the equation,
7x2 -- 3x -- 2 = 0, then the value of
\[{\alpha \over {1 - {\alpha ^2}}} + {\beta \over {1 - {\beta ^2}}}\] is equal to :
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Given, 7x2 -- 3x -- 2 = 0
\[ \therefore \] \[\alpha \] + \[\beta \] = \[{3 \over 7}\]
\[\alpha \] β \beta β = - 2 7 {2 \over 7} 7 2 α 1 − α 2 + β 1 − β 2 {\alpha \over {1 - {\alpha ^2}}} + {\beta \over {1 - {\beta ^2}}} 1 − α 2 α + 1 − β 2 β = α + β − α β ( α + β ) 1 − α 2 − β 2 + α 2 β 2 {{\alpha + \beta - \alpha \beta \left( {\alpha + \beta } \right)} \over {1 - {\alpha ^2} - {\beta ^2} + {\alpha ^2}{\beta ^2}}} 1 − α 2 − β 2 + α 2 β 2 α + β − α β ( α + β ) = 3 7 + 2 7 ( 3 7 ) 1 − ( α + β ) 2 + 2 α β + ( − 2 7 ) 2 {{{3 \over 7} + {2 \over 7}\left( {{3 \over 7}} \right)} \over {1 - {{\left( {\alpha + \beta } \right)}^2} + 2\alpha \beta + {{\left( { - {2 \over 7}} \right)}^2}}} 1 − ( α + β ) 2 + 2 α β + ( − 7 2 ) 2 7 3 + 7 2 ( 7 3 ) = 3 7 + 2 7 ( 3 7 ) 1 − ( 3 7 ) 2 + 2 ( − 2 7 ) + ( − 2 7 ) 2 {{{3 \over 7} + {2 \over 7}\left( {{3 \over 7}} \right)} \over {1 - {{\left( {{3 \over 7}} \right)}^2} + 2\left( { - {2 \over 7}} \right) + {{\left( { - {2 \over 7}} \right)}^2}}} 1 − ( 7 3 ) 2 + 2 ( − 7 2 ) + ( − 7 2 ) 2 7 3 + 7 2 ( 7 3 ) = 27 16 {{27} \over {16}} 16 27 Answer the question to unlock