Question
Find the number of solutions of the equation xx−1+x1−x=137.
Answer: Option A
:
A
If we suppose xx−1=a.
Then, xx−1=1a
And the equation becomes a+1a=137
Now we know that for a real number a :
a+1a is greater than or equal to 2 "OR" less than or equal to -2.
Therefore a+1a can never be 137 (less than 2 but greater than -2).
Hence the given equation has no solution i.e., the number of solutions is zero.
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:
A
If we suppose xx−1=a.
Then, xx−1=1a
And the equation becomes a+1a=137
Now we know that for a real number a :
a+1a is greater than or equal to 2 "OR" less than or equal to -2.
Therefore a+1a can never be 137 (less than 2 but greater than -2).
Hence the given equation has no solution i.e., the number of solutions is zero.
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