Find the minimum value of 3x? 2 + 1 / 2x? 2 (x ≠ 0)

Find the minimum value of 3x? 2 + 1 / 2x? 2 (x ≠ 0)

3x²+1/2x²
3 x 2 × 1 / 2 x 2 = 3 / 2 is a fixed value, so sum has a minimum value
3x? + 1 / 2x? ≥ 2 root number (3 / 2) = root number 6

It is known that y = 2x 2 + 3x-5,1. X belongs to [- 5, - 3]. Find the maximum and minimum values, and the range of values It is known that y = 2x 2 + 3x-5,1. X belongs to [3,3]. There are two problems in finding the maximum and minimum value and the range of values,

y'=4x+3
Let y '= 0, x = - 3 / 4
1.f(-5)=30,f(-3)=4
Therefore, the maximum value is 30, the minimum value is 4, and the range is [4,30]
2.f(-3/4)=-49/8,f(-3)=4,f(3)=22
Therefore, the maximum value is 22, the minimum value is - 49 / 8, and the range is [- 49 / 8,22]

Find the minimum value of the quadratic function y = 1 / 2x 2 + 3x + 2 / 1

For quadratic functions, you should remember the combination of numbers and shapes, especially the maximum and minimum value. When the parabola opening is upward, the function has a minimum value, and the y value corresponding to the symmetry axis is the minimum value

Solving quadratic equation of one variable by collocation method: 2x 2 + 1 = 3x

2x²+1=3x
2x²+1-3x=0
x²-3/2x+(3/4)^2-(3/4)^2+1/2=0
(x-3/4)^2=1/16
X-3 / 4 = 1 / 4 or x-3 / 4 = - 1 / 4
X = 1 or x = 1 / 2

When x > 0 and Y > 0, if x and y are both 3 times larger than the original, how does the value of fraction 3x? - 7Y? 2 / 2x + 3Y change? If x and y are reduced to the original When x > 0, Y > 0, if both X and y are 3 times larger than the original, how does the value of fraction 3x? - 7Y? / 2x + 3Y change? What if x and y are reduced to 1 / k?

When x > 0, Y > 0, if x and y are expanded by 3 times, the value of fraction 3x? - 7Y? 2 / 2x + 3Y will be increased by 3 times, because the denominator can give a square of common factor 3, that is 9, and the numerator can propose 3, so the whole time sharing will be tripled
Similarly, the whole fraction will be reduced by 1 / K, and the molecule can put forward the square of 1 / K, and the molecule will be reduced by 1 / K, so the whole fraction will be reduced by 1 / K

To solve the fractional equation: (2x? + 3x + 2) / (2x? - 3x-2) = (2x? - 5x + 3) / (2x? + 5x-3) With the steps of multiplication on both sides,

By multiplying both sides, the result is: 4x ^ 4 + 16x? + 13X? + X-6 = 4x ^ 4-16x? + 17x? + X-6
Merge similar items: 32x? - 4x? = 0, i.e. x? 2 (8x-1) = 0
The solution is: X1 = 0, X2 = 1 / 8

Given that x > 0, Y > 0, if x and y are tripled, then fraction 3x2 − 7y2 How does the value of 2x + 3Y change?

If x and y are tripled, then the fraction 3x2 − 7y2
The value of 2x + 3Y is increased by 3 times,
Answer: formula 3x2 − 7y2
The value of 2x + 3Y is increased by 3 times

When the value of 3x + 5 / x + 3 is 0, calculate the value of fraction x 2 - 2x-3 / x-3

（x+3)/(3X+5)=0
=>x=-3
(x-3)/(x²-2x-3)=(x-3)/((x-3)(x+1)=1/(x+1)=-1/2

If x? - 3x-1 = 0, find the value of the fifth power of fraction 2x - the fourth power of 5x - X and the third power of - x

Sorry, I haven't learned fractions yet!

Given that 2x-y = 10, find [(x 2 + y 2) - (X-Y) 2 + 2Y (X-Y)] / 4Y Given that 2x-y = 10, finding [(x 2 + y 2) - (X-Y) 2 + 2Y (X-Y)] / 4Y is known as 2x-y = 10, and finding [(X-Y) + y (X-Y)] / 4Y / 4Y is divided by 4Y

Predigest [(x 2 + y 2) - (X-Y) 2 + 2Y (X-Y)] / 4Y [(X-Y + y 2) - (X-Y) 2 + 2Y (X-Y)] / 4Y = [x? + y? - (x? + y? - 2XY) + 2xy-2y] / 4Y = [x? + y? - x? - y? + 2XY + 2xy-2y] /