The equation: 5x + 3Y = 54 has several positive integer solutions

The equation: 5x + 3Y = 54 has several positive integer solutions

To solve the Diophantine equation, XY is a positive integer
From 5x + 3Y = 54
1.x=3,y=13
2.x=6,y=8
3.x=9,y=3
So there are three sets of solutions

When m is an integer, the solution of the equation 12mx − 53 = 12 (x − 43) is a positive integer?

If we solve the equation 12mx − 53 = 12 (x − 43), remove the denominator, we get 3mx-10 = 3 (x-43), remove the bracket, we get 3mx-10 = 3x-4, transfer the term and merge the similar terms, we get x (m-1) = 2, the coefficient is 1, we get x = 2m − 1, ∵ the solution of the equation is a positive integer, ∵ x > 0 and is a positive integer, ∵ 2m − 1 > 0 and M is a positive integer, ∵ M-1 is a positive divisor of 2, that is, M-1 = 1 or 2, ∵ M = 2 or 3

The domain of the function f (x) = LG (X-2) is______ ．

In order to make the function f (x) = LG (X-2) meaningful, X-2 ﹥ 0 and ﹥ x ﹥ 2 are necessary. The domain of definition of function f (x) = LG (X-2) is: (2, + ∞), so the answer is: (2, + ∞)

If (x ^ m ÷ x ^ 2n) &# - 179; △ x ^ M-N and & # - 188; X & # - 178; are of the same kind and 2m + 5N = 6, find the value of M, n

Answer: the value of n is = 30

Given that f (x) has inverse function on (- ∞, 0) and f (x-1) = x ^ 2-2x, find F - &# 185; (2)

f(x-1)=x^2-2x+1-1=(x-1)^2-1
So f (x) = x ^ 2-1
Let f (x) = 2
That is, x ^ 2-1 = 2
x=3
Because f (x) has an inverse function on (- ∞, 0)
So x = - root 3
That is, F - &# 185; (2) = - radical 3

If the function f (x) = | x + 1 | - a | - X-1 | is odd, then the value of real number a is

f(-x)=|-x+1|-a|-x-1|=|x-1|-a|x+1|=-f(x)=-|x+1|+a|x-1|
(|x+1|+|x-1|)a=|x+1|+|x-1|
a=1

Given that the maximum value of function f (x) = - x ^ 2 + ax + 1 / 2-A / 4 in the interval [0,1] is 2, find the value of function a

f（x）=-x^2+ax-a/4+1/2
=-The maximum value of (x-a / 2) ^ 2 + (a ^ 2-A + 2) / 4 in the interval [0,1] is 2,
1)0

Let p be an orthogonal matrix and | P | = - 1, it is proved that: - 1 is the eigenvalue of P

The eigenvalues of orthogonal matrices, except 1 and - 1, must appear in pairs according to λ, 1 / λ, so | P | = (- 1) ^ k, K is the algebraic multiplicity of eigenvalue - 1

When is life plural

This can not be summarized one by one, but if it is used as "human life", that is, the number of human lives, the plural is used;
In addition, if it is clear that "several kinds of life" is countable in the modifier, we should use lives

Calculate LG (10 ^ 3-10 ^ 2) =?

lg(10^3-10^2)=lg(1000-100)=lg(900)=lg(3²×10²)＝lg3²＋lg10²＝2×lg3＋2＝2﹙1＋lg3﹚.