This is a Test of Mathematics Solution Subjective 71 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
Consider the following simultaneous equations in x and y :
where is a real constant. Show that these equations admit real solutions in x and y.
... (i)
... (ii)
[ replacing x in terms of y. ]
This is a 3rd degree polynomial over y.
Now as we know any odd degree polynomial has at least one real root.That is why y has also at least one real root.Now for that particular root we get also real.
Conclusion: &
admits real solutions in x and y.
This is a Test of Mathematics Solution Subjective 71 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
Consider the following simultaneous equations in x and y :
where is a real constant. Show that these equations admit real solutions in x and y.
... (i)
... (ii)
[ replacing x in terms of y. ]
This is a 3rd degree polynomial over y.
Now as we know any odd degree polynomial has at least one real root.That is why y has also at least one real root.Now for that particular root we get also real.
Conclusion: &
admits real solutions in x and y.