Solve \((8-t)^2 < \left(t^2-3 t-10\right)\)

Solve \((8-t)^2 < \left(t^2-3 t-10\right)\)
  1. \(\left(\frac{74}{13}, 8\right]\)
  2. \(\left(\frac{74}{13}, \infty\right)\)
  3. \((8, \infty)\)
  4. \([8, \infty)\)

Solution

It is given that, \(\begin{array}{rlrl} & & (8-t)^2 < t^2-3 t-10 \\ \Rightarrow & 64-16 t+t^2 < t^2-3 t-10 \\ \Rightarrow & 13 t > 74 \\ \Rightarrow & t > \frac{74}{13} \\ \Rightarrow & t \in\left(\frac{74}{13}, \infty\right) \end{array}\) Hence, option (b) is correct.

Asked in: AP EAMCET 2020 (21 Sep Shift 2)

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