which equation is equivalent to $sqrt{x^{2}+81}=x + 10$?\n$x + 9=x + 10$\n$x + 9=x^{2}+20x +…

which equation is equivalent to $sqrt{x^{2}+81}=x + 10$?\n$x + 9=x + 10$\n$x + 9=x^{2}+20x + 100$\n$x^{2}+81=x^{2}+100$\n$x^{2}+81=x^{2}+20x + 100$

which equation is equivalent to $sqrt{x^{2}+81}=x + 10$?\n$x + 9=x + 10$\n$x + 9=x^{2}+20x + 100$\n$x^{2}+81=x^{2}+100$\n$x^{2}+81=x^{2}+20x + 100$

Answer

Answer:

D. $x^{2}+81=x^{2}+20x + 100$

Explanation:

Step1: Square both sides of the equation

Given $\sqrt{x^{2}+81}=x + 10$, squaring both sides gives $(\sqrt{x^{2}+81})^2=(x + 10)^2$.

Step2: Simplify both sides

The left - hand side $(\sqrt{x^{2}+81})^2=x^{2}+81$. The right - hand side, using the formula $(a + b)^2=a^{2}+2ab + b^{2}$ where $a=x$ and $b = 10$, we have $(x + 10)^2=x^{2}+2\times x\times10+10^{2}=x^{2}+20x + 100$. So $x^{2}+81=x^{2}+20x + 100$.