How to do the maximum value of 4x square × (6-x Square)

How to do the maximum value of 4x square × (6-x Square)

Let a = x & # 178;
Then a > = 0
Original formula = 4A (6-A)
=-4(a²-6a)
=-4[(a-3)²-9]
a>=0
So a = 3
The maximum value of the original formula = - 4 × (- 9) = 36

Finding the maximum value of - 3x & # 178; + 12x + 1 by formula method

-3x²+12x+1
=-3(x²-4x)+1
=-3(x²-4x+4)+13
=-3(x-2)²+13≤13
When x = 2, the maximum value of the function is 13

It is proved that the square of; - x + 4x-5 is always less than 0

That's the formula. The result will come out at once~

The value of X & # 178; - 4x + 5 is greater than 0, which is proved by matching method

x^2-4x+5=(x-2)²+1
Because the square of X-2 is not less than 0, plus 1 is not less than 1, so it is greater than 0
Respondent: 100000wsm | level 4 | 2011-9-22 22:08 | prosecution
x²-4x+5=（x²-4x+4）+1=(x-2)²+1
Because (X-2) &# 178; is always greater than or equal to 0, the value of (X-2) &# 178; + 1 is always greater than 0
Please take the answer and support me

1. Prove that the value of a ^ 2-2a + 3 is always positive by matching method 2. Find the minimum value of 2x ^ 2-3x + 1 online, etc. quick!

1（a-1）²+2
∵（a-1）²≥0
∴（a-1）²+2＞0
2min = 2 (x-0.75) &# 178; - 0.125
When x = 0.75, the minimum value is -0.125

The value of x ^ 2-2x + 3 is always greater than 0

x²-2x+3
=x²-2x+1+2
=(x-1)²+2≥2>0
So the value is always greater than 0

Matching method 2x & # 178; + 6x-2 = 0

x²+3x=1
x²+3x+9/4=13/4
(x+3/2)²=13/4
x=-3/2+√13/2 x=-3/2-√13/2

Using collocation method to find the maximum value of polynomial 2x & # 178; - 4xy + 4Y & # 178; + 6x + 25
Matching method

2x²－4xy+4y²+6x+25
=x²－4xy+4y²+x²+6x+9+16
=(x-2y)²+(x+2)²+16
When x = - 2, y = - 1, there is a minimum value of 16

Help mathematical collocation method 2x & # 178; + 6x + 6 = 4

[example] to solve the equation: 2x & # 178; + 6x + 6 = 4
Analysis: the original equation can be sorted out as: X & # 178; + 3x + 1 = 0, and (x + 1.5) &# 178; = 1.25 can be obtained by formula, which can be solved by square root
2x²+6x+6=4
(x+1.5)²=1.25

Is the square of x plus 4x plus 3 equal to (x + 1) (x + 3)?

x²+4x+3=(x²+x)+(3x+3)=x(x+1)+3(x+1)=(x+1)(x+3)