Ask a math problem: given a + A ^ (- 1) = 3, use two methods to find the value of a ^ 5 + A ^ (- 5) According to the example, Given a + A ^ (- 1) = 3, find the value of a ^ 3 + A ^ (- 3) Because [a + A ^ (- 1)] ^ 2 = a ^ 2 + a ^⊥ 222 [2 / 3] (- 2) + 2 = 9, So a ^ 2 + A ^ (- 2) = 9-2 = 7, So a ^ 3 + A ^ (- 3) = [a + A ^ (- 1)] [a ^ 2 + A ^ (- 2)] - [⊥ 222 [3 / 3] a + A ^ (- 1)] = 3 * 7-3 = 18

Ask a math problem: given a + A ^ (- 1) = 3, use two methods to find the value of a ^ 5 + A ^ (- 5) According to the example, Given a + A ^ (- 1) = 3, find the value of a ^ 3 + A ^ (- 3) Because [a + A ^ (- 1)] ^ 2 = a ^ 2 + a ^⊥ 222 [2 / 3] (- 2) + 2 = 9, So a ^ 2 + A ^ (- 2) = 9-2 = 7, So a ^ 3 + A ^ (- 3) = [a + A ^ (- 1)] [a ^ 2 + A ^ (- 2)] - [⊥ 222 [3 / 3] a + A ^ (- 1)] = 3 * 7-3 = 18

In the same way
The fourth power of a + one fourth power of a = 5
(fourth power of a + one fourth power of a) * a + A ^ (- 1) = a ^ 5 + A ^ (- 5) + A ^ 3 + A ^ (- 3)
a^5+a^(-5)=5*3-18=-3

Three points a (- 2,0), B (2,2), C (0,1) are known. Two methods are used to prove that the three points are collinear?

Proof: 1
y=(1/2)x+1
Substituting point B into the equation, we can know that ABC three points are collinear
2. Vector method: ab = (4,2), AC = (2,1)
∴AB=2AC
The ABC three points are collinear

Given a > 0, if three points a (1, - a), B (2, a ^ 2), C (3, a ^ 3) in the plane are collinear, then a=
A ^ 2: the square of a
A ^ 3: the third power of a

If three points are collinear, the slope of line AB and line BC are the same
∴(a²+a)/(2-1)=(a³-a²)/(3-2)
∴a³-2a²-a=0
a(a²-2a-1)=0
∵a>0
∴a²-2a-1=0
∴a=1+√2

If (ob-oc) · (OB + oc-2oa) & nbsp; = 0, then △ ABC is ()
A. Isosceles triangle with ab as base B. isosceles triangle with BC as base C. right triangle with ab as hypotenuse D. right triangle with BC as hypotenuse

Let the midpoint of BC be D, ∵ (ob-oc) · (OB + oc-2oa) & nbsp; = 0, ∵ CB · (2od-2oa) = 0, ∵ CB · 2ad = 0, ≁ CB ⊥ ad, so the midline on the BC side of △ ABC is also a high line. So △ ABC is an isosceles triangle with BC as the bottom, so B is selected