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  • Let S be the set of all real roots of the equation,  <img alt="3^{x}(3^{x}-1)+2=\left | 3^{x}-1 \right |+\left | 3^{x}-2 \right |." src="https://entrancecorner.oncodecogs.com/gif.latex?3%5E%7Bx%7D%283%5E%7Bx%7D-1%29&plus;2%3D%5Cleft%20%7C%203%

Let S be the set of all real roots of the equation,  3^{x}(3^{x}-1)+2=\left | 3^{x}-1 \right |+\left | 3^{x}-2 \right |. Then S _____.
Option: 1 is a singleton set
Option: 2 is an empty set
Option: 3 contains at least four elements
Option: 4 contains exactly two elements
 

Answers (1)

best_answer

\text{Put }3^x=t

\\t\left(t-1\right)+2=\left|t-1\right|+\left|t-2\right|\\t^2-t+2=\left|t-1\right|+\left|t-2\right|

Only one point of intersection to the right of y-axis (we need postive t as 3x > 0)

Hence, singleton set

Correct Option (1)

Posted by

vishal kumar

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