Question

The solution set for 5v^2 – 125 = 0 is

Answer 1

The solution set for the equation 5v^2 - 125 = 0 is {-5, 5}.

Step-by-step explanation:

The solution set for the equation 5v^2 - 125 = 0 can be found by applying the square root property. By isolating the variable v, we have v^2 = 125/5. Taking the square root of both sides, we get v = ±√(125/5), which simplifies to v = ±5. Therefore, the solution set is {-5, 5}.

Answer 2

`\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ 5v^2-125=0\qquad \boxed{125=5^3=5\cdot 5^2}\qquad 5v^2-5(5^2)=0 \\\\\\ 5(v^2-5^2)=0\implies v^2-5^2=0\implies (v-5)(v+5)=0 \\\\\\ v= \begin{cases} 5\\ -5 \end{cases}`