Question

HELP ASAP ITS TIMED

Answer 1

Answer:

$x+10=x^2+2x+1$

Step-by-step explanation:

Given equation:

$\sqrt{x+10}-1=x$

Add 1 to both sides:

$\implies \sqrt{x+10}-1+1=x+1$

$\implies \sqrt{x+10}=x+1$

Square both sides:

$\implies (\sqrt{x+10})^2=(x+1)^2$

$\implies \sqrt{x+10}=(x+1)(x+1)$

Simplify:

$\implies \sqrt{x+10}=x(x+1)+1(x+1)$

$\implies \sqrt{x+10}=x^2+x+x+1$

$\implies x+10=x^2+2x+1$

Answer 2

Answer:

  x + 10 = x² + 1

(third option listed)

Step-by-step explanation:

assuming that you meant: $\sqrt{x+10-1}=x$  , because otherwise there would be no equivalent relationships,

(goal: isolate x on one side of the equation whilst having x on the other side of the equation also, like the equation in the question)*

   x + 10 = x² + 1

        -1            -1

   x + 10 - 1 = x²

  $\sqrt{x+10-1} =\sqrt{x^2}$                  [find √ of both sides to isolate x]

$\sqrt{x+10-1} =x$         (equation in problem)

       

{note: there's no reason to not simplify the equation to $\sqrt{x+ 9$, but the question leaves the equation that way, so I didn't simplify it either}

*I used this goal to decide which equations seemed about right, and then trying to test things out in my head