Given (m-n) ^ 2 = 8, (M + n) ^ 2 = 2, then = m ^ 2 + n ^ 2=________ .

（m-n)^2=8
m²+n²-2mn=8 (1)
(m+n)^2=2,
m²+n²+2mn=2 (2)
(1) + 2
2(m²+n²)=10
m²+n²=5

Given that x ^ 4 + MX ^ 3 + nx-16 has factors (x-1) and (X-2), find the value of M and n

When x = 1 or 2, x ^ 4 + MX ^ 3 + nx-16 = 0
Substituting x = 1, x = 2 into x ^ 4 + MX ^ 3 + nx-16 = 0 respectively
1+m+n-16=0 16+8m+2n—16=0
m=-5 n=20

It is known that the lengths of three sides of △ ABC are a, B, C respectively, and satisfy (root sign) A-3 + (absolute value) B-4 + C (square) - 10C + 25 = 0. Try to judge the shape of △ ABC

(radical) A-3 + (absolute value) B-4 + C (square) - 10C + 25 = 0,
(radical) A-3 + (absolute value) B-4 + (C-5) (flat = 0,
a-3=0,b-4=0,c-5=0
a=3,b=4,c=5
c^2=a^2+b^2
ABC is a right triangle

Several math problems (real numbers)
1: If a and B are irrational numbers and a + B = 3, then the values of a and B can be (just fill in one group)
2: If the ratio of the length of an isosceles triangle to the length of its base is 5:8 and the height of its base is three times the root sign 3, then the perimeter of the isosceles triangle is , with an area of__ .

1: If a and B are irrational numbers and a + B = 3, then the values of a and B can be__ 3-root 3, root 3____ (just fill in one group)
2: If the ratio of the waist length to the base length of an isosceles triangle is 5:8 and the height of its base is three times the root sign 3, then the circumference of the isosceles triangle is__ 18 times root 3____ , with an area of_ 36_____ .
The height on the bottom edge is three times root number 3, so the waist length is five times root number 3, and the bottom edge is eight times root number 3
The perimeter is 18 times the root sign 3
The area is 36

The second chapter of the first volume "real number" preview experience high reward!
To preview the experience of 100-250 words or so, a good high reward!

Through the preview of the second chapter of real number, although there is no teacher's help, but I still roam in the digital world, once again experienced the "expansion of numbers". This preview brought me a lot of harvest: there are many practical problems, maybe the first step of mathematical exploration, can bring us countless inspiration and interest, step by step into the door of the palace of mathematics, and finally won the laurel of success!

Real number preview experience
Better have more words

Real numbers are divided into rational numbers and irrational numbers. Rational numbers include 0, finite decimals, integral fractions, and roots that can be opened. Irrational numbers include infinite circulant and infinite non circulant decimals, and roots that cannot be opened (such as root sign 2 and root sign 5). To tell the truth, this chapter is just more difficult to understand at the beginning, and the key is to grasp the concept and not

Preview and talk about the feeling after preview

Real numbers are divided into rational numbers and irrational numbers. Rational numbers include 0, finite decimals, integral fractions, and roots that can be opened. Irrational numbers include infinite cyclic and infinite non cyclic decimals, and roots that cannot be opened (such as root number 2 and root number 5). They are very easy to learn

The preview of the first chapter of the eighth grade mathematics volume of Beijing Normal University Edition
Preview the Pythagorean theorem,

I have a deep understanding of Pythagorean theorem. It makes me understand one of the main bases of right triangle, and it is widely used in production and life
Pythagorean theorem has a very long history. Almost all ancient civilizations have studied it. Therefore, some historians regard it as one of the greatest scientific discoveries of mankind
Pythagorean theorem is an old and widely used theorem. With its simple and beautiful form, rich and profound content, it fully reflects the harmonious relationship of nature. Therefore, it has become the most important theorem in mathematics
After previewing Pythagorean theorem, I understand some strange and interesting rules. For example, if a, B and C are Pythagorean arrays and N are positive integers, then Na, Nb and NC are Pythagorean arrays

If three mutually unequal rational numbers can be expressed as either 1, a, a + B or 0, B, Ba, then a= ，b= ．

∵ three mutually unequal rational numbers are expressed in the form of 1, a + B, a, and 0, Ba, B. the numbers of these two arrays are equal. One of a + B and a is 0, and one of Ba and B is 1. However, if a = 0, Ba will be meaningless, and a ≠ 0 can only be a + B = 0, that is, a = - B Ba = - 1. Only b = 1, then a = - 1. So the answer is: - 1, 1

If the function y = f (x) satisfies f (a + b) = f (a) + F (b) for all real numbers a and B, and f (1) = 8, find f (- 1 / 2)

If f (a + b) = f (a) + F (b) let a = b = 0, then f (0) = f (0) + F (0), then f (0) = 0, if a = b = 1 / 2, then f (1) = f (1 / 2) + F (1 / 2) = 8, then f (1 / 2) = 4, if a = 1 / 2, B = - 1 / 2, then f (0) = f (1 / 2) + F (- 1 / 2), then f (- 1 / 2) = f (0) - f (1 / 2) = 0-4 = - 4

Given (m-n) ^ 2 = 8, (M + n) ^ 2 = 2, then = m ^ 2 + n ^ 2=________ .