If M = 2 - √ 3, n = √ 3 - √ 2, then the size relation of Mn is

If M = 2 - √ 3, n = √ 3 - √ 2, then the size relation of Mn is

Method 1: proof method
M-N=(2+√2)-2√3
Compare the size of (2 + √ 2) and 2 √ 3
∵ both are greater than 0
(2+√2)^2=6+4√2
〖(2√(3))〗^2=12=6+6=6+4√2.25
So (2 + √ 2)

If the equation MX + 3-nx − 3 = 8xx2 − 9 holds for any x (x ≠ ± 3), then Mn = ()
A. 8B. -8C. 16D. -16

From the meaning of the question: (m − n) x − 3 (M + n) x2 − 9 = 8x2 − 9, and the equation MX + 3-nx − 3 = 8xx2 − 9 holds for any x (x ≠ ± 3)}, we can get: M-N = 8, - 3 (M + n) = 0, the solution is: M = 4, n = - 4, Mn = - 16

If M / (x 3) - N / (x-3) = 8x / (x ^ 2-9) (x is not equal to plus or minus 3), then the value of Mn is? If M / (x + 3) - N / (x-3) = 8x / (x ^ 2-9) (x is not equal to plus or minus 3), then the value of Mn is? For detailed explanation

In the left side of the equal sign, m and (x + 3) multiply (x-3) at the same time, and N and (x-3) multiply (x + 3) at the same time. In this way, the denominator becomes x ^ 2-9. Now, the denominators on the left and right sides of the equal sign are x ^ 2-9, so the molecules are equal. That is, m (x-3) - n (x + 3) equals 8x. The left side is simplified to get (m-n) x-3 (M + n). Because the right side of the equal sign is 8x, M-N = 8 and M + n = 0