Question

hellppp pleasee

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

Given: m2 + 6 = 10
Conjecture: m = 2 is the ONLY solution

Answer 1

i thought it was true

Answer 2

do you mean \(m2\) or \(m^2\)?

Answer 3

\[m ^{2}\]

Answer 4

then it is false.. there are two solutions possible
why.. because the equation is of second degree -> means -> m can be two values
\[
m^2+6=10\\
m^2=4
\]
now, remember that
\[(a)^2=a^2\qquad\text{and}\qquad(-a)^2=a^2\]
hence,
\[m=\pm\sqrt{4}\]
so, m=+2
or m = -2
(two possible solutions which can work)

Answer 5

thanks