Question

The number of positive integral solutions of $x^2+9<(x+3{)}^2<8x+25$, is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (D)

We have, $x^2+9<{(x+3)}^2<8x+25$
$\Rightarrow$ $x^2+9<x^2+6x+9<8x+25$
$\Rightarrow$ $x^2+9<x^2+6x+9$
and $x^2+6x+9<8x+25$
$\Rightarrow$ $6x>0$ and $x^2-2x-16<0$
$\Rightarrow$ $x>0$ and $1-\sqrt{17}<x<1+\sqrt{17}$
$\Rightarrow$ $0<x<1+\sqrt{17}$
$\therefore x=1,2,3,4,5$