Question 381 of 455MediumMCQ
If α=β but α2=5α−3 and β2=5β−3, then the equation having α/β and β/α as its roots is Solutions · 1
Official solution
We have \[{\alpha ^2} = 5\alpha - 3\] and \[{\beta ^2} = 5\beta - 3;\]
\[ \Rightarrow \alpha \,\,\& \,\,\beta \] are roots of
equation, x2=5x−3 or x2−5x+3=0
\[\therefore\] \[\alpha + \beta = 5\] and \[\alpha \beta = 3\]
Thus, the equation having \[{\alpha \over \beta }\,\,\& \,\,{\beta \over \alpha }\] as its roots is
\[{x^2} - x\left( {{\alpha \over \beta } + {\beta \over \alpha }} \right) + {{\alpha \beta } \over {\alpha \beta }} = 0\]
\[ \Rightarrow {x^2} - x\left( {{{{\alpha ^2} + {\beta ^2}} \over {\alpha \beta }}} \right) + 1 = 0\]
or 3x2−19x+3=0 Answer the question to unlock