Given (A2 + B2) (A2 + b2-10) = - 25, find the value of A2 + b2de

Given (A2 + B2) (A2 + b2-10) = - 25, find the value of A2 + b2de

Let a ^ 2 + B ^ 2 = t
Then t (T-10) + 25 = 0
That is, (T-5) ^ 2 = 0
t=5
That is, a ^ 2 + B ^ 2 = 5
In fact, we should pay attention to observation and holistic thinking,

Given the function f (x) = x2 LNX ax, a ∈ R. (I) when a = 1, find the minimum value of F (x); (II) if f (x) > x, find the value range of A

(I) when a = 1, f (x) = x2-lnx-x, f ′ (x) = (2x + 1) (x − 1) X. when x ∈ (0, 1), f ′ (x) < 0; when x ∈ (1, + ∞), f ′ (x) > 0. The minimum value of F (x) is f (1) = 0. (II) f (x) > x, that is, f (x) - x = x2 LNX - (a + 1) x > 0

On factorization
Square of 1. (a + b) - 4 (a + B-1) (factorization)
2. Factorization of square (B + 1) of a to square (a + 1) of B
Square factorization of 3.4A (B-A) - B
4. Given (the square of a + the square of B) (the square of a + the square of B-1) = 12, find the value of the square of a + the square of B (with process)
5. The perimeter of square a is 96cm longer than that of square B, and their area is 960 square cm different. Find the side length of the two squares (with process)
6. Find the value of positive integers a and B satisfying the equation A's Square - B's Square = 23
In the evening

Original problem: 1. (a + b) square-4 (a + B-1) (factorization) 2. A square (B + 1) - b square (a + 1) factorization 3. 4a (B-A) - b square factorization 4. Known (a square + b square) (a square + B Square-1) = 12, find the value of a square + b square (with process) 5

If the image of a quadratic function is known to pass through points - (1,22), (0, - 8), (2,8), the expression of the quadratic function is obtained
The quadratic function is y = - 2x + 12x-8

Let the image of a quadratic function pass through points a (- 1, - 22), B (0, - 8), C (2,8); find the expression of the quadratic function. Let the quadratic function be y = ax & # 178; + BX + C; substitute the coordinates of three points into A-B + C = - 22. (1) C = - 8. (2) 4A + 2B + C = 8. (3) substitute C = - 8 into (1) and (3) to get A-B = - 14. (4) 4A + 2B

Using the collocation method to solve X & # 178; + 8x-20 = 0

x²+8x-20=0
x²+8x+16-36=0
(x+4)²=36
x+4=±6
x+4=6
x=2
Or x + 4 = - 6
x=-10
So x = 2 or x = - 10

If the vertex of quadratic function y = - 2x ^ 2 + MX - 3 is on the X axis, then M =?

The vertex of quadratic function y = - 2x ^ 2 + MX - 3 is on the X axis
Then there is only one intersection point between the parabola and the x-axis
△=m²-4[（-2）×（-3）=0
m²-24=0
m²=24
m=±2√6
∴ m=±2√6

Elimination -- solution of linear equations of two variables
｛3X+4Y=1
｛3X-5Y=19

It's about 3x
3X+4Y-(3X-5Y)=1-19
9Y=-18
Y=-2
Substituting the above formula
3X-8=1
X=3
So x = 3, y = - 2

The distance from the x-axis is equal to 2. Find the trajectory equation satisfying the condition

Y = 2 or y = - 2

Solving practical problems with linear equation of one variable
In a clothing workshop, there are 60 people, each of whom processes one piece of clothing or two pairs of trousers per hour. How to arrange the work so that the clothes and trousers can match each other? (one piece of clothing goes with one pair of trousers)

Let x people make clothes and 60-x people make trousers
x=2(60-x）
We get x = 40
60-x=20
A: 40 people make clothes and 20 people make pants

What is the total land area in China?
How much land does each person occupy?

China's total land area ranks third in the world, but the per capita land area is only one third of the world's per capita land. China's cultivated land area is 128.2331 million hectares, which is decreasing at a rate of about 1.3 million hectares every year. The per capita cultivated land is only 43% of the world's per capita cultivated land, less than 1 / 15 of Canada's and only 1 / 2 of India's, The amount of soil loss of cultivated land in China is 3.3 billion tons per year, accounting for 1 / 3 of the total cultivated land. The forest coverage rate is lower than that of most countries in the world (16.55% in 2000), ranking 120th among more than 200 countries and regions in the world. The average net growth rate of forest land is only 2.66%, with an average annual growth of 2.4m3/ha, Most of the grasslands are located in arid, semi-arid and alpine regions, with low content of soil organic matter, low proportion of high-quality grassland and serious degradation. At present, the yield per unit area of available grassland has decreased by 30% - 50% compared with that in 1960s
The total amount of water resources in China is 2.8 trillion m3 / A, of which the surface water is about 2 trillion m3 / A and the groundwater is about 0.8 trillion m3 / A. the total amount of water resources ranks sixth in the world, but the per capita ownership is only 1 / 4 of the world's per capita, ranking 109th in the world, It makes the situation of water resources in China more complicated. 45% of China's land is located in the arid zone with less than 400 mm precipitation, and the national precipitation is mainly concentrated in June to September, accounting for 70-90% of the annual precipitation. Therefore, more than 70% of China's water resources are composed of temporary floods
Although China is rich in mineral resources, its per capita share is only 58% of the world's per capita level, ranking 53rd in the world