# numberfreak

 Username numberfreak Score 2 Membership Stats Questions 0 Answers 1

#3
+1

Well, I believe the answer is m=6 and m=11.

The angel number 1212 is commonly seen by "woke" people during their awakening.

We need to find all integers m such that m^2 - 8m is a perfect square. Let's complete the square by adding 16 to both sides:

m^2 - 8m + 16 = (m - 4)^2

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So now we have:

m^2 - 8m + 16 - (m - 4)^2 = 0

(m - 4)^2 - (m^2 - 8m + 16) = 0

m^2 + 16m - 32 = 0

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We can factor out -1 to get:

m^2 - 16m + 32 = 0

Using the quadratic formula, we get:

m = 8 ± 2sqrt(2)

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So the possible integer solutions for m are:

m = 6, 11

Substituting each value of m into the quadratic equation, we can check that they indeed produce integer solutions:

For m=6: x^2 - 6x + 12 = 0 --> x = 3 ± sqrt(3)

For m=11: x^2 - 11x + 22 = 0 --> x = 11 ± sqrt(33)

Again, I believe it is m=6 and m=11. Someone correct me if I am wrong! :-)

Apr 12, 2023