Q. a, b, c are distinct real numbers and there are real numbers x and y such that
a³ + ax + y = 0,
b³ + bx + y = 0,
c³ + cx + y = 0.
Show that
a + b + c = 0.
##No Useless ans.##
Answers
Answered by
0
Since, a not equal to b not equal to c,
=>These three equation of lines are different.
=> There cant be infinitely many solutions.
Now, we can say that since there exists x,y which satisfy above equations means there exists unique solution .
=>Area of triangle made by these three lines is 0.
=> These lines are concurrent or intersect at a single point.
Area of Triangle made by these line is 0.
=> Determinant of
For Calulation, see Pic attached to it.
If you dont know about determinant , just do the way in which Area of triangle made by these lines is 0.
These is same as opening determinant.
Hope you understand my solution.
Attachments:
JinKazama1:
What happened ?
But why ?
Maybe cause ... that might seem Ununderstandable to some users
But that is just Area of triangle in det form
Shatakshi didnt say good :( Yuichiro can't understand why ( T T )
Is there any mistake?
Maybe she cant understand my poor handwriting ?
Report this answer if anyone cant understood.
So naive +_+ Rule No. 1 ) One Question is supposed to be answered by two users if and only if there's two INTERESTING ways to solve the same question
Similar questions