Given x + y = 4, xy = - 12, then x ^ 2 + y ^ 2 = x ^ 2-xy + y ^ 2 = (X-Y) ^ 2=

Given x + y = 4, xy = - 12, then x ^ 2 + y ^ 2 = x ^ 2-xy + y ^ 2 = (X-Y) ^ 2=

Given x + y = 4, xy = - 12, then x ^ 2 + y ^ 2 = x ^ 2-xy + y ^ 2 = (X-Y) ^ 2=
x^2+y^2=（x+y）^2-2xy=16-2*(-12)=40
X^2-XY+Y^2=(x-y)^2-3xy=16-(-12)=52
(x-y)^2=(x+y)^2-4xy=16-4（-12）=64

X / 3 + Y / 4 > = 2 √ (XY / 12), this is how to solve the basic inequality, and finally equal to XY
The problem is: given that X and Y belong to R *, and satisfy X / 3 + Y / 4 = 1, then the maximum value of XY is. This is a basic inequality problem

Dizzy, isn't this almost finished?
x/3+y/4≥2√(xy/12)
If and only if x / 3 = Y / 4, the equal sign holds
I.e. 1 ≥ 2 √ (XY / 12)
Square 1 ≥ 4 (XY / 12)
So XY ≤ 3
That is, the maximum value of XY is 3

Given f (x + y) = f (x) f (y), f (1) = 2, find f (2 / 1) + F (3 / 2) + F (4 / 3) +... + F (1999 / 2000) =?
Sorry, the last one is f (2000 / 1999)

According to the law of the first few terms, the last term should be f (2001 / 2000). From F (x + y) = f (x) f (y), we can get: F (x + y) / F (x) = f (y) f (2 / 1) + F (3 / 2) + F (4 / 3) +... + F (2001 / 2000) = f [(1 + 1) / 1] + F [(2 + 1) / 2] + F [(3 + 1) / 3] +... + F [(2000 + 1) / 2000] = f (1) +... F (1) = 2000f (1

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Simple easy

Given the sum of the first n terms of the arithmetic sequence {an} and Sn = n & # 178; finding an

When we know Sn and find an, we need to remember that an = sn-sn-1
Let n = 1 be an = Sn = n & # 178; = 1
When n > = 2, an = sn-sn-1 = n & # 178; - (n-1) ^ 2 = 2N-1
A1 = 1 is also consistent with this equation
Then an = 2N-1

Given: X & sup2; + xy = 3, XY + Y & sup2; = - 2, find: 2x & sup2; - xy-3y & sup2;

x²+xy=3 (1)
xy+y²=-2(2)
(1)×2-(2)×3
(2x²+2xy)-(3xy-3y²)=6-(-6)
2x²-xy-3y²=12

The trunk of a truck is 8m long, 3M wide, and can be loaded with coal 1.2 high. How many cubic meters of coal does this truck transport at one time? If each cubic meter of coal weighs 1.5 tons, how many tons does a truck have?

1. 8 * 3 * 1.2 = 28.8m3
2. 1.5 * 28.8 = 43.2 tons

When multiple lines intersect at one point, how many pairs of vertex angles and how many pairs of adjacent complementary angles are there? Please try to complete the table below

How many pairs of vertex angles do n lines intersect? How many pairs of adjacent complementary angles do n lines intersect? (in the same plane, how many pairs of vertex angles do n lines intersect? How many pairs of adjacent complementary angles do n lines intersect?) answer: first of all, if there are only two lines, the two lines are not parallel, then there will be an intersection, two pairs of vertex angles and four pairs of adjacent complementary angles

For XY, f (x + y) = f (x) + F (y) and for x > 0, f (x)

Let x = 0, y = 0, then f (0) = 2F (0), f (0) = 0, let x = x, y = - x, then f (0) = f (x) + F (- x), odd shift, if - f (x) is greater than 0, then f (- x) is greater than 0, combined with the known, increasing, F2 = 2F1 = 6, F3 = F2 + F1 = 9, then F-3 = - F3 = - 9

What are the physical properties of pure water?
From the color, smell, state, boiling point, freezing point to answer

The beauty of professional team mathematics for you at the first time
Pure water is a colorless, odorless, tasteless and transparent liquid. Pure water is not easy to conduct electricity. Under normal pressure, the freezing point (freezing point) of water is 0 ℃ and the boiling point is 100 ℃. At 4 ℃, the mass of 1 cubic centimeter of water is 1g, and the density is the highest. Cooling water to 0 ℃ can form ice and increase its volume, which is 1.09 times of the original volume. Heating water to 100 ℃ can turn water into steam, The volume of water increases 1600 times. Water has a strong ability to dissolve many substances. Water contains dissolved air. The life of aquatic organisms depends on dissolved oxygen
Hope to help you!