No matter what value x takes, the value of algebraic formula 2 times the square of x-4x + 5 is always positive

No matter what value x takes, the value of algebraic formula 2 times the square of x-4x + 5 is always positive

2x^2-4x+5
=2x^2-4x+2+3
=2(x-1)^2+3
Because (x-1) ^ 2 > = 0
SO 2 (x-1) ^ 2 + 3 > = 3
So 2x ^ 2-4x + 5 is always positive

Solving the system of inequalities 1 / 3x + 5Y = - 1, y-3x = - 9.4
1/3x+5y=-1
y-3x=-9.4
(solution inequality system) write process, you can consider bonus

It's called an equation, not an inequality
x+15y= -3
y=3x-9.4
x+45x-141= -3
46x=138
x=3
y=-0.4

If the solution of inequality {5x + 3Y = m-1,3x + 5Y = m + 1} satisfies x + y < 0, try to find the maximum integer value of M

By adding 5x + 3Y = M-1 and 3x + 5Y = m + 1, we get
8x+8y=2m,
So x + y = m / 4,
From x + y

Given that positive real number XY satisfies x + y = 1, find the minimum value of 1 / (2x + y) + 4 / (2x + 3Y)

x. Y ∈ R and X + y = 1,
∴1/(2x+y)+4/(2x+3y)
＝1^2/(2x+y)+2^2/(2x+3y)
≥(1+2)^2/[(2x+y)+(2x+3y)]
＝9/[4(x+y)]
＝9/4.
So (2x + y): 1 = (2x + 3Y): 2 and X + y = 1,
When x = 1 / 3, y = 2 / 3,
The minimum value is 9 / 4