It is known that the equation x ^ 2 + 2x-m + 1 = 0 has no real number roots. This paper proves that x ^ 2 + MX + 2x + 2m + 1 = 0 must have two unequal real number roots

It is known that the equation x ^ 2 + 2x-m + 1 = 0 has no real number roots. This paper proves that x ^ 2 + MX + 2x + 2m + 1 = 0 must have two unequal real number roots

If X & # 178; + 2x + (1-m) = 0 has no real root, then
△=4-4（1-m）=4m

If the equation x2-2x-m + 1 = 0 has no real roots, we prove that the equation X2 - (2m-1) x + M2-2 = 0 has two unequal real roots

It is proved that: ∵ equation x2-2x-m + 1 = 0 has no real root, ∵ (- 2) 2-4 × 1 × (- M + 1) ＜ 0, the discriminant of the root of M ＜ 0, X2 - (2m-1) x + M2-2 = 0 △ = (2m-1) 2-4 (M2-2) = - 4m + 8, ∵ m ＜ 0, ∵ - 4m + 8 ＜ 0 is obtained, that is, ∵ equation X2 - (2m-1) x + M2-2 = 0 has two unequal real roots

Tianfu mathematics 2010 issue 18 seventh grade synchronous rational number unit test paper answer is optional, the important is the question of the paper
It's as like as two peas.
A lot of points!

Children's shoes:
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If the scale of a plan is 1:1000, the actual distance is equal to ()

1000 times

Famous sayings of mathematicians and celebrities

For me, studying mathematics is as natural as breathing. Erdos, because the structure of the universe is the most perfect and the wisest creation of God, nothing will happen if there is no certain maximum or minimum law in the universe

After watching a chess match, it takes one minute, two minutes, five minutes and ten minutes for a, B, C and D to cross the bridge. Because it's dark, they have to use a flashlight to cross the bridge, but they only have one flashlight in total, and the bridge's load capacity is limited, so they can only bear the weight of two people at most, that is, they can cross two people at most at a time How can the bridge be as short as possible? You can arrange it for them. What's the shortest time?

According to the minimum time required for four people to cross the bridge, it can be concluded that the two people who spend the least time should be allowed to cross the bridge first, and it will save time for them to send lights back and forth. Therefore: (1) 1 minute and 2 minutes to cross the bridge first (at this time, it takes 2 minutes); (2) 1 minute to come back (at this time, it takes 3 minutes); (3) 5 minutes and 1

The following phenomena belong to translation and rotation
A raise the national flag B turn the faucet C sit on the slide d the electric fan turns

In translation, a raises the national flag and C takes the slide,
Belongs to the rotation is (b screw faucet D fan rotation)

Given that the nonzero vectors a and B satisfy the norm of A-B = the norm of a + B = the norm of λ· B (λ > = 2), then the maximum angle between A-B and a + B is?

Modules of A-B = modules of a + B
∴ (a-b)²=(a+b)²
∴ 4a.b=0
∴ a⊥b
Modules of a + B = modules of λ· B
∴ (a+b)²=(λ·b)²
∴ a²+b²+2a.b=λ²b²
∴ a²=(λ²-1)|b|²
(a+b)·(a-b)=|a|²-|b|²=(λ²-2)|b|²
|a-b|²=|a+b|²=|a|²+|b|²=λ²|b|²
∴ cos
=(a+b)·(a-b)/(|a+b|*|a-b|)
=(λ²-2)|b|²/(λ²|b|²)
=(λ²-2)/λ²
=1-2/λ²
∵ λ≥2,
∴ λ²≥4,
∴ -1/λ²∈[-1/4,0)
∴ 1-2/λ²∈[1/2,1)
That is, when the angle is the largest, the cosine value is 1 / 2
The angle is 60 degrees

In the isosceles triangle ABC, D is a point on the edge of BC, De is parallel to AC, DF is parallel to AB, and ab = be + AE = de + DF is proved

Because: De / / AF, DF / / EA;
So:

If sinaxcosa = 1 / 8 and π / 4 < a < π / 2, what is cosa Sina equal to?

sinacosa = sin2a/2 = 1/8,
∵ sin2a = 1 / 4, and ∵ π / 2