Question

Lucas and tony were trying to solve the equation: \[x^2=16x 25\] lucas said, "the \[x^2\] term is isolated, so i'll take the square root of both sides and solve." tony said, "i'll solve using the quadratic formula with \[a=1\], \[b=16\], and \[c=25\]." whose solution strategy would work?

a. Only Lucas's
b. Only Tony's
c. Both
d. Neither

Answer 1

Lucas's strategy of taking the square root of both sides would not work to solve the equation x^2 = 16x + 25. Tony's strategy of using the quadratic formula with a = 1, b = 16, and c = 25 is the correct approach.

Step-by-step explanation:

To solve the equation x^2 = 16x + 25, both Lucas and Tony have different strategies. Lucas suggests taking the square root of both sides, while Tony suggests using the quadratic formula. Let's analyze their strategies:

Lucas's Strategy:

If we take the square root of both sides, we get x = √(16x + 25). However, this is not the correct approach because it only solves part of the equation, and we need to consider both the positive and negative square roots. Additionally, we cannot take the square root of 16x + 25 as it is not a perfect square. Therefore, Lucas's strategy would not work.

Tony's Strategy:

The equation x^2 = 16x + 25 is a quadratic equation in the form ax^2 + bx + c = 0. In this case, a = 1, b = 16, and c = 25. Tony suggests using the quadratic formula x = (-b ± sqrt(b^2 - 4ac)) / (2a). This is the correct approach to solve the quadratic equation, so Tony's strategy would work.