Question

Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

Given: m2+6=10m2+6=10
Conjecture: m=2

Answer 1

The conjecture m = 2 is true for the given equation m^2 + 6 = 10, but it is not always true. A counterexample would be m^2 + 7 = 10.

Step-by-step explanation:

The given equation is m^2 + 6 = 10. To determine whether the conjecture m = 2 is true or false, we substitute m = 2 into the equation:

(2)^2 + 6 = 10

Simplifying, we get 10 = 10, which is true. Therefore, the conjecture m = 2 is true for this equation.

Counterexample: If the equation were m^2 + 7 = 10, we can substitute m = 2 into the equation:

(2)^2 + 7 = 10

Simplifying, we get 11 = 10, which is false. This counterexample shows that the conjecture m = 2 is not always true.

Answer 2

I think that if you plug in 2 for m in the given equation, you can solve to see if it is true or not.