Question

Set of all real values of $x$ satisfying the inequation $\sqrt{x^2-5x-24}>x+2$

• A. $(-\infty ,8]$
• B. $[8,\infty )$
• C. $(-\infty ,-3]$
• D. $(-\infty ,\frac{-28}{9}]$

Answer 1

The correct option is D $(-\infty ,\frac{-28}{9}]$

$\sqrt{x^2-5x-24}>x+2$

Squaring both sides

$x^2-5x-24>(x+2{)}^2{x}^2-5x-24>x^2+8x+49x<-28x<\frac{-28}{9}$

But

$x^2-5x-24>0(x-8)(x+3)>0x>-3,x>8$

$x\in (-\infty ,\frac{-28}{9}]$