Let a and B be rational numbers, and a and B satisfy the equation a squared + 2B + B times root sign 2 = 17-4 times root sign 2, and find the value of a + B

Let a and B be rational numbers, and a and B satisfy the equation a squared + 2B + B times root sign 2 = 17-4 times root sign 2, and find the value of a + B

a. B is a rational number, so a ^ 2 + 2b is a rational number,
A ^ 2 + 2B + B root sign 2 = 17-4 root sign 2, so:
a^2+2b=17.(1)
b=-4.(2)
Substituting (2) into (1) gives:
a^2=17-2b=17+2*4=25
a=±5.（3）
So a + B = 5-4 = 1
Or a + B = - 5-4 = - 9

Who can help me solve this problem: A, B are rational numbers, and satisfy: a square + 2B + 2 times the root sign b = 17-4 times the root sign 2, find the value of a + B

The original formula can be changed into:
a^2 +(2 +√2)b = 25 +(2 +√2)*(-4),
That is, a ^ 2 = 25, B = - 4,
So: a = ± 5, B = - 4
Therefore, when a = 2, a + B = 5 - 4 = 1,
When a = - 2, a + B = - 5 - 4 = - 9

If a and B are rational numbers and a and B satisfy a square + 2B + root sign 2 × B = 17-4 root sign 2, calculate the value of a + B

The root number was 2 × 2 B + 2 b;
a^2+b(2+√2)-25+8+4√2=0;
(a^2-25)+(2+√2)(b+4)=0;
a. B is a rational number, a = 5 or - 5, B = - 4;
A + B = 1 or - 9

It is known that a and B are rational numbers and satisfy the equation 5 - √ 3A = 2B + 2 / 3 ×√ 3-A to find the value of ab 5-√3a=2b-2√3/3-a 5+a-2b=√3(a-2/3) There are rational numbers on the left, so are rational numbers on the right √ 3 is a rational number only when multiplied by 0 So A-2 / 3 = 0, a = 2 / 3 Right = 0, so the left is equal to 0 So 5 + a-2b = 0 b=(5+a)/2=17/6 a=2/3,b=17/6 I want to ask: how does the formula 5 + a-2b = radical 3 (a - two thirds) come from? And why is the left rational, so is the right rational? Why is multiply by 3

The first question: moving to get
2： Because the left and right sides are equal
3： Because the root 3 itself is an irrational number, it is irrational to multiply any number

Given that a and B are rational numbers and satisfy the equation 5-radical 3A = 2B + 2 times the root sign 3-1, find the value of the third-order root sign minus 6 (a + b)

If a, B are rational numbers, 5 - √ 3A = 2B + 2 √ 3-1, then 2b-1 = 5, - a = 2, B = 3, a = - 2, so √ - 6 (a + b) = √ - 6x (3-2) = √ - 6

If a, B, C are positive, we prove that 2 {(a + b) / 2 - √ AB} ≤ 3 {(a + B + C) / 3-cubic root ABC} There is another one: known n > 0, proof: 3N + 4 / (n square) ≥ 3 times the third root sign 9

0

Under the condition that ab = a × B under the root of the equation is true

A ≥ 0 and B ≥ 0

Given AB > 0, try to compare the size of cubic root a-cubic root B and cubic root a-b Is the size of cubic root a minus cubic root B and cubic root a-b

3 = A-B + 3 (AB) ^ (1 / 3) - B ^ (1 / 3)] ^ 3 = A-B + 3 (AB) ^ (1 / 3) (a ^ (1 / 3-B ^ (1 / 3)) [(a-b) ^ (1 / 3)] ^ 3 = (a-b) [a ^ 1 / 3) - B ^ (1 / 3)] ^ 3 - [(a-b) ^ (1 / 3)] ^ 3 = 3 (AB) ^ (1 / 3) (a ^ (1 / 3-B ^ (1 / 3)) (1) because of AB > 0, so when a > b > 0, or 0 (a-b) ^ (a-b) ^ (a-b) ^ (a-b) ^ (a-b) ^ (a-b) ^ (a-b) ^ ((1 / 3) when b > a > 0, or 0

It is known that a and B are rational numbers, and satisfy the equation that 3A = 2B + 2 / 3 times 3-A under the root sign of equation 5, try to find the values of a and B

5-√3a=2b+2√3/3-a
5+a-2b=√3(a+2/3)
There are rational numbers on the left, so are rational numbers on the right
√ 3 is a rational number only when multiplied by 0
So a + 2 / 3 = 0, a = - 2 / 3
Right = 0, so the left is equal to 0
So it's 0-2b
b=(5+a)/2=13/6
a=2/3,b=13/6

It is known that a and B are rational numbers and satisfy the equation: 5-radical 3A = 2B + 3 / 2 radical sign 3. Find the value of a + B

5-√3a=2b+3/2√3
2b=5-(a+3/2)√3
Because a and B are rational numbers, so:
a=-3/2 b=5/2
a+b=1