Question

Given 51 = 43 + 2m², show and explain why this equation has two solutions.

A) m = 2 and m = -2
B) m = 7 and m = -7
C) m = 5 and m = -5
D) m = 1 and m = -1

Answer 1

Starting with the equation 51 = 43 + 2m², we isolate the term with m, leading to 4 = m². Taking the square root of both sides gives us the two solutions m = 2 and m = -2.

Step-by-step explanation:

The given equation is 51 = 43 + 2m². To find the solutions for m, the equation needs to be simplified and solved for m² first. Subtracting 43 from both sides of the equation gives us 51 - 43 = 2m², which simplifies to 8 = 2m². Then we divide both sides by 2, resulting in 4 = m². Taking the square root of both sides, we get two possible solutions for m: √4 = 2 and -√4 = -2, which corresponds to choice A: m = 2 and m = -2.