Question

$\sqrt{2x+9}+x=13$ gives $x=$

• A. 12
• B. 13
• C. 8
• D. 9

Answer 1

The correct option is C 8

The given equation $\sqrt{2x+9}+x=13$ can be rewritten as $\sqrt{2x+9}=13-x$

Squaring both sides of the equation $\sqrt{2x+9}=13-x$, we get:

$(\sqrt{2x+9}{)}^2=(13-x{)}^2\Rightarrow 2x+9={13}^2+x^2-(2\times 13\times x)(\because ({a-b)}^2=a^2+b^2-2ab)\Rightarrow 2x+9=169+x^2-26x\Rightarrow 169+x^2-26x-2x-9=0\Rightarrow x^2-28x+160=0$

$\Rightarrow x^2-20x-8x+160=0\Rightarrow x(x-20)-8(x-20)=0\Rightarrow (x-8)(x-20)=0\Rightarrow x-8=0,x-20=0\Rightarrow x=8,x=20$

Hence, $x=8$ or $x=20$.