Answer
$x$= -0.62 and 1.62
Work Step by Step
Given equation-
$x - \sqrt {x+1}$ = $0$ , in the interval [-1,5]
i.e. $x $ = $\sqrt {x+1}$, (Adding $\sqrt {x+1}$ on both the sides)
Now squaring on both the sides-
$x^{2} $ = $x+1$
i.e. $x^{2}-x-1$ = $0$ in the interval [-1,5]
We are asked to find all solutions 'x' that satisfy $-1 \leq x \leq 5$, so we use a graphing calculator to graph the equation in a viewing rectangle for which the x-values are restricted to the interval [-1,5] .
Graphing $y$ = $x^{2}-x-1$, using graphing calculator-
There are two $x-intercepts$ in the given interval, $x= -0.62$ and $1.62$
Thus in the given interval, $x= -0.62$ and $1.62$
