Knowing the function y 3 and root number x 5 plus 4 root number 6 x, what is the maximum value of th

If y=3 (x-5)+4 (6-x), then there are 5 x 6 because [ (x-5)]+6-x)] =1, so let (x-5)=sin , 6-x)=cos , so y=3sin +4cos =5sin( +tan =4 3, when + = 2, y gets the maximum value of 5.

The maximum value of the function is 5.

Method 1: When finding the maximum value of the form ab+cd, apply the Cauchy inequality solution.

According to Cauchy's inequality: (ab+cd) a +c (b +d), ad=bc with an equal sign).

Take a=3, c=4, b= (x-5), d= (6-x), and get it.

3√(x-5)+4√(6-x)]²3²+4²)[x-5)²+6-x)²]=25(x-5+6-x)=25

So the maximum value of 3 (x-5)+4 (6-x) is 5

Method 2: When finding the maximum value of ASIN + BCOS, apply functions and formulas to solve the problem.

Because y 3 is the root number x-5 plus 4 and the root number 6-x=3 (x-5)+4 (6-x), and (x-5) +6-x) =1, take (x-5)=sin , 6-x)=cos, and get it.

3 (x-5)+4 (6-x)=3sin +4cos =5sin( +5, (where tan =4 3).

So the maximum value of 3 (x-5)+4 (6-x) is 5

First of all, both sides are squared at the same time, you can get y squared = -7x + 75, and then move -7x over to get y square + 7x = 75, so the maximum value is 75...

Because. x^2-5x+6

x^2+5x)+6

x+5 2) 2+49 4

When x=-5 2, such as key culture, take the maximum value of 49 4

So. The maximum value of the original bright sky = (49 4) = 7 2

Method 1: Laughing at the meaning of the high formula, then x-5>=0, 6-x>=0

That is, the definition field of the function is {x 5

The original formula is equal to y=x+4-x 2

x^2+x+4

x^2-x-4)

x^2-x-(1/2)^2-(1/2)^2-4]-[x-1/2)^

x-1/2)+

Therefore, when x=1 2, y is the largest to answer Zhenbu, and the largest is to see that I have to work so hard

y=√(2x-3)+√8-4x)=√2*√(x-3/2)+2*√(2-x)

From the beginning of the defeat to the change of Cauchy does not wait for the quiet judgment of the dry round.

y^2=[√2*√(x-3/2)+2*√(2-x)]^2

x2+4x+5=(x+2)2+1,x2-4x+8=(x-2)2+4, the combination of numbers and shapes is equivalent to finding the minimum value of the sum of the coarse defects on the x-axis to (-2,1) and (2,2), which is equivalent to the distance from (-2,-1) to (2,2).

According to the rock type, the minimum value of the distance between the two points can be obtained as 5

Solution: Let the root number (x-5) = U, and the root number (6-x) = v, then u 2+v 2 = 1, u, v belong to [0, 1].

Therefore, y=3u+4v, the following can be used discriminant method, number combination method, trigonometric substitution method, etc.

The following triangulation substitution is used: set the root number under (x-5) = sint, and the root number under (6-x) = cost

Then y=3sint+4cost=5sin(t+a) (auxiliary angle formula), so the maximum value is 5

Solution: Derived from the question.

x－5≥0①

6－x≥0②

Get 5 x 6

Y is maximum when x (5, 6) 2.

y(max)＝3√