Question

Let $y^2-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals to _____ (Give the answer up to three decimal paces).

• A. 5.732

Answer 1

The correct option is A 5.732
Given $y^2-2y+1=x$ ...(i)

and $\sqrt{x}+y=5$ ...(ii)

From (i) and (ii), we get,

$y^2-2y+1=(5-y{)}^2$

$\Rightarrow y^2-2y+1=25+y^2-10y$

$\Rightarrow 8y=24$

$\Rightarrow y=3andx=4$

$\therefore x+\sqrt{y}=4+\sqrt{3}=4+1.732=5.732$