Practicing Success
Practicing Success
CUET Preparation Today
The least positive integer for which x $4^x+8^{(2/3)(x-2)}-72-4^{x-3/2}≥0$ is non-negative, is ______. |
| 4 |
We have, $4^x+8^{(2/3)(x-2)}-72-4^{x-3/2}≥0$ $⇒2^{2x}+2^{2x-4}-2^{2x-3}-72≥0$ $⇒2^{2x}+\frac{2^{2x}+}{16}-\frac{2^{2x}+}{8}-72≥0⇒2^{2x-4}≥\frac{24}{5}$ Clearly, 4 is the smallest positive integer satisfying this inequation. |
