Party A and Party B start from ab at the same time. Party A rides a bicycle and Party B rides a motorcycle. They drive at a constant speed along the same route. After starting, they meet at 3 o'clock. It is known that Party B is 84 kilometers more than party a when they meet. After meeting, Party B arrives at place a at 5 / 4. Q: what are the speeds of Party A and Party B

Party A and Party B start from ab at the same time. Party A rides a bicycle and Party B rides a motorcycle. They drive at a constant speed along the same route. After starting, they meet at 3 o'clock. It is known that Party B is 84 kilometers more than party a when they meet. After meeting, Party B arrives at place a at 5 / 4. Q: what are the speeds of Party A and Party B

Let the velocity of a be x, then the velocity of B be x + 84 △ 3 = x + 28
3x=5/4(x+28)
12x=5x+140
7x=140
x=20
The speed of a is 20 km / h, the speed of B is 20 + 28 = 48 km / h

Given three points a (- 1,0,1) B (2,4,3) C (5,8,5) in space, it is proved that three points are on a line

Vector AB (3,4,2)
Vector BC (3,4,2)
So the vector AB is parallel to the vector BC
And because there's a common point B
So ABC is collinear

Given √ A-3) + 2 √ 6-2a = B + 8, find the value of √ B to the power of A

The solution is: (A-3) + 2 √ (6-2a) = B + 8
If the domain A-3 ≥ 0, the solution a ≤ 3
6-2a ≥ 0, a ≤ 3
So a = 3
b= -8
A times radical B = - 2
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In the eighth grade mathematics problem [1], we know that the real numbers a and B satisfy a ^ 2 = 2-2a, B ^ 2 = 2-2b, and a ≠ B, then we can find B / A + A / b =?
[2] Given that P ^ 2-2p-5 = 0, 5q ^ 2 + 2q-1 = 0, where P and Q are real numbers and P ≠ 1 / Q, find the value of P ^ 2 + 1 / Q ^ 2?
Step by step

(1) It is known that a and B are the two roots of the quadratic equation x ^ 2 = 2-2x
a+b=-2,ab=-2,
So a / B + B / a = (a ^ 2 + B ^ 2) / (AB) = (2-2a + 2-2b) / (- 2) = (4-2 * (- 2)) / (- 2) = - 4,
(2) According to the coefficients of the two equations, if the two roots of the first equation are P1 and P2, then the two roots of the second equation are 1 / P1 and 1 / P2, and the relationship between the roots and the coefficients leads to P1 + P2 = 2, P1 * P2 = - 5
Because P is not equal to 1 / Q,
So p ^ 2 + 1 / Q ^ 2 = P1 ^ 2 + P2 ^ 2 = (P1 + P2) ^ 2-2p1 * P2 = 2 ^ 2-2 * (- 5) = 14