The number of values of a for which the system of equations 
and 
has only one solution where 
are real, is
Text Solution
Verified by ExpertsA
Let 
be a solution of the system for some 
. Then, 
is also a solution. So, the system will have unique solution only if
Putting 
and 
in 
, we get 
.
Putting 
and 
in 
, weget
when 
and 
when 
.
CASE I - When 
In this case, given equations become
Now, 
and 
Putting 
in 
, we get 
.
Thus, for 
, the system has unique solution 
.
CASE II - When 
In this case, the system of equations is
Clearly, 
and 
satisfy these equations.
So, the system does not have unique solution.
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