Exams Joint Entrance Examination Mathematics Quadratic Equations and Inequalities Question 125 Question 125 of 157 Medium MCQ
If \[\alpha \] and \[\beta \] be two roots of the equation
x2 -- 64x + 256 = 0. Then the value of
\[{\left( {{{{\alpha ^3}} \over {{\beta ^5}}}} \right)^{1/8}} + {\left( {{{{\beta ^3}} \over {{\alpha ^5}}}} \right)^{1/8}}\] is :
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x2 -- 64x + 256 = 0
\[\alpha \] + \[\beta \] = 64, \[\alpha \] β \beta β = 256 ( α 3 β 5 ) 1 / 8 + ( β 3 α 5 ) 1 / 8 {\left( {{{{\alpha ^3}} \over {{\beta ^5}}}} \right)^{1/8}} + {\left( {{{{\beta ^3}} \over {{\alpha ^5}}}} \right)^{1/8}} ( β 5 α 3 ) 1/8 + ( α 5 β 3 ) 1/8 = α 3 8 β 5 8 + β 3 8 α 5 8 {{{\alpha ^{{3 \over 8}}}} \over {{\beta ^{{5 \over 8}}}}} + {{{\beta ^{{3 \over 8}}}} \over {{\alpha ^{{5 \over 8}}}}} β 8 5 α 8 3 + α 8 5 β 8 3 = α + β ( α β ) 5 8 {{\alpha + \beta } \over {{{\left( {\alpha \beta } \right)}^{{5 \over 8}}}}} ( α β ) 8 5 α + β = 64 ( 256 ) 5 8 {{64} \over {{{\left( {256} \right)}^{{5 \over 8}}}}} ( 256 ) 8 5 64 Answer the question to unlock