If 3(np2 +24) =2np2, find the positive value of n

Answer 1

To find the positive value of n, we can first simplify the equation.

Expanding the equation:
3(np^2 + 24) = 2np^2
3n * np^2 + 72n = 2np^2
3n^2p^2 + 72n = 2np^2

Now, let's isolate the terms with n:
3n^2p^2 - 2np^2 + 72n = 0

Factorizing n out:
n(3np^2 + 72) - 2p^2(3n - 36) = 0

Setting each term equal to zero:
n = 0 (since 3np^2 + 72 = 0 → 3n(0) + 72 = 0 → 0 + 72 = 0)
or
3np^2 + 72 = 0
3n(p^2 + 24) = 0

Now, we have two cases to consider:

1) n = 0
2) p^2 + 24 = 0

For the second case, we are finding the value of p that makes the expression zero:
p^2 + 24 = 0

Subtracting 24 from both sides:
p^2 = -24

Since we are only interested in the positive value of n, we can conclude that n = 0.

Answer 2

This very first step is wrong:
3(np^2 + 24) = 2np^2
3n * np^2 + 72n = 2np^2

Should be
3np^2 + 72 = 2np^2

Answer 3

Apologies for the error in the initial step. Let's correct it and continue solving the equation.

Starting with the correct equation:
3np^2 + 72 = 2np^2

To isolate the terms with n, we can move all the terms with n to one side of the equation and the constant terms to the other side:

3np^2 - 2np^2 = -72

Simplifying the left side of the equation:
np^2 = -72

Now, we need to find the positive value of n. Since the squared term p^2 is positive (assuming n is a real number), the left side can only be negative if n is negative.

Therefore, there is no positive value of n that satisfies the equation 3(np^2 + 24) = 2np^2.