Senior 2 Math Inequality 2 Easy Choice .

Since the equation holds and x,y are both positive, then 0<8 x<1,0<1 y<1 finds the range of x,y, x>8,y>1

Equation deformation: x+8y=xy

Recipe: (x 2) 2+x+1+y 2+8y+16=(x 2) 2+xy+y 2+17

x 2+1) 2+(y+4) 2=(x 2+y) 2+17 multiplied by 4 at the same time, (x+2) 2+(2y+8) 2=(x+2y) 2+68

Therefore, (x+2y) 2=(x+2) 2+(2y+8) 2-68 Since x,y are both positive, then x>8,y>1

Then: (x+2) 2>100,(2y+8) 2>100x+2y) 2>132

x+2y>12

Personally, I think that the minimum value should be infinitely close to 12, but not equal to 12

For the common question type, (8 x) + (1 y) = 1, multiply the required formula by (8 x) + (1 y) and the value is unchanged, then the multiplication formula is 10 + 16 y x + x y Using the mean inequality, the minimum value of the pull is 18 and choose a

It's very simple, why is it so annoying to solve x+2y?

Since (8 x) + (1 y) = 1, then x+2 = (x+2) ((8 x) + (1 y)) = 10 + 16 y x + x y

by mean inequalities.

The above is greater than or equal to 10 + 8 = 18

Therefore, select [a].

From the positive numbers x and y satisfying the condition of (8 x) + (1 y) = 1, x>8 can be obtained

y>1 then x+2y>10

Fundamental inequality.

8/x=1-(1/y)

8/x<1

x>81/y=1-(8/x)

1/y<1

y>1

Triangular exchange of dollars.

Let a= 6cos and b= 3sin (known conditions can be a2 6+b 2 3=1).

Using the formula: asinx+bcosx=root(a2+b2)*sin(+where the "auxiliary angle" satisfies the condition "tan =b a", and the quadrant position of the auxiliary angle is determined by the quadrant position of the points (a, b).

The value of a+b is 3sin(+

When sin( +=-1, a+b takes the minimum value -3, and this kind of problem mostly uses the commutation method.

Think of square A and square 2b as the two sides of a triangle with sides of a and (root 2)b. According to the sum of the two sides is greater than the third side, the third and 9th smallest is a+(2)b

That's kind of the idea, because if you write like that, you don't know if it's 2b squared or 2 times the square of b.

You should be aware of that, right?

The detailed answer is as follows: Absolutely! Give me a rating.

x>0xsquared》0

x square + 4x + 4 > 4x + 4

x+2) squared" 4x+4

x+2> hept sign (4+4x) = 2 hept sign (1+x) both sides of the hept sign (1+x) are divided by 2 at the same time to get 1+x 2 "geng number (1+x)".

The idea of this problem should be that you can square both sides of the formula at the same time.

Reverse Extrapolation:

1+x）^1/2 < 1+x/2

Square on both sides. 1+x < 1+x+x^2/4

0 < x^2/4

This question is proven.

Use the analytical method to prove that the two sides are squared first, and then the difference is sufficient.

1.y=2 x 2 and z=3x+2 x 2-1 derivative z'=3-4 x 3 another z'=0 x=(3 4) (1 3).

Substituting x into the equation yields a minimum value of 3(3 4) (1 3)+2 (9 16)) 1 3)-1

2 Original=24x-6x 3 Derivative=24-18x 2 =0 x=(4 3) 1 2 bar x substitution.

The resulting maximum value is 24x(4 3) 1 2 -16x(1 3) (1 2).

LZ, give you the answer! It was too much effort for me to write on a computer, I wanted to write it for you, but I gave up!

1.6x 2-17x+12>0 and 2x 2-5x+2>0 solve 2nd order equations.

2.6x 2-17x+12<0 and 2x 2-5x+2<0!=0

4.Combine the results and you're the answer!

It's really hard to write.,It's too hard.。。。