a. B is a rational number, and √ (7-times root sign 3) (note brackets,) is a root of the equation x ^ + ax + B = 0, find a + B If I can't do it, I'll be scolded to death I'll thank you

a. B is a rational number, and √ (7-times root sign 3) (note brackets,) is a root of the equation x ^ + ax + B = 0, find a + B If I can't do it, I'll be scolded to death I'll thank you

Is it √ (7-4 times root 3)?
In this way, 7 is divided into 3 + 4, that is, the square of (√ 3) + the square of 2, so the original formula can be changed into the square of (2 - √ 3)
SO 2 - √ 3 is its root
Then, because a and B are rational numbers, it is easy to judge that the other root is 2 + √ 3
So a = 4, B = 1 (Veda theorem) so a + B = 5

Given that a and B are rational numbers, x = √ 5 + 1 is a solution of the equation x to the third power - ax + B = 0, find the value of a and B

x=√5+1
x-1=√5
Square on both sides
x²-2x+1=5
x²=2x+4
x³-ax+b=0
x(x²-a)=-b
x(2x+4-a)=-b
2x²+(4-a)x=-b
2(2x+4)+(4-a)x=-b
(8-a)x=-b-8
Because 8-A and - B-8 are rational numbers
X is an irrational number
Rational number multiplied by irrational number equals rational number
Then the rational number can only be 0
So 8-A = 0, - B-8 = 0
a=8,b=-8

The x power of Y is equal to 100 and the 20th power of 3 + the 10th power of 9 is equal to the Y power of 2 times 9. It is a system of equations to find the values of X and y

The 20th power of 3 + the 10th power of 9 is equal to the Y power of 2 times 9
9^10+9^10=2*9^y
y=10
y^x=100
10^x=10^2
x=2
x=2,y=10

It is known that the solution of the system of equations {3x + 5Y = m + 2,1} about X, y satisfies x + y = - 10,3, and the value of the algebra M & # 178; - 2m + 1 is obtained

Formula 3x + 5Y = m + 21
Formula 2x + 3Y = m 2
From Formula 1 to formula 2, we get the following results
X + 2Y = 2,3
X + y = - 10 4
From Formula 3 to 4, we can get the following results
If y = 12, we can get the following formula by 4
x=-22
Taking x = - 22, y = 12 into formula 2, we get the following result:
-44+36=m
m=-8
m²-2m+1=(m-1)² m=-8 m-1=-9
So (m-1) ² = 81