The problem of quadratic radicals. Quadratic Radical Problems?

Answer: 9 5 means 9 times 5, which can be written as 9 5, which is no problem, but the landlord's understanding behind has been deviated.

The teacher said: When the quadratic radical is multiplied, the rational number is multiplied by the rational number, and the root number is multiplied by the root number.

In fact, it is said that when both quadratic radicals have coefficients, such as (9 5) x (2 2) = (9x2) x ( 5x 2) = 18 10

At this point, you are very confused, why is the same level of operation, why not multiply from left to right?

For example, 2a b 3ab, I believe you should understand that the result is 6a b, why not multiply 2, a, b, 3, a, b in turn?

When multiplying algebraically, the coefficients are multiplied as the product coefficients, and then the factors with the same base are multiplied. Actually, this practice is not wrong, you should remember that in multiplication though there is"Sibling operations, from left to right"The rules that you should also understand in multiplication are there"The associative law of multiplication".In the just 2a b 3ab=6a b just now, this property is used, and the answer is quickly obtained.

Going back to the example just now, (9 5) means 9x 5, if you do this in sequence 9x 5 can only be this result, because 9 5 is already the simplest form, so in the quadratic root calculation, it requires the rules like the teacher said. Such as:

9√5)x(2√2)=(9x2)x(√5x√2)=18√10.

If you don't understand it, please feel free to communicate more.

For example, 9 (5) 2 (3), I don't know if you can see it.

I mean 9 root number 5 divided by 2 root number 3, is there a multiplication sign hidden between 9 root number 5 and 2 root number 3? (Yes).

If there is not a multiplier sign hidden, then why do they represent 9 root numbers 5 and 2 root numbers 3 (is), respectively

The teacher said: Multiply rational numbers with rational numbers, and multiply root numbers with root numbers. (Yes).

But I always felt that there was a multiplier sign between them. If they have, they are sibling operations, calculated from left to right (not necessarily) (by multiplication exchange rate).

Then the rational number is multiplied by the rational number, and the root number is multiplied by the root number. That's right.

Well, I knew I was wrong, but I fought with my teacher for a long time about it, and she still didn't give me a specific reason. So I'm very depressed, and it's not a good feeling to do this kind of topic. Because I didn't understand.

Find a specific reason: the rational number multiplies the rational number, and the root number multiplies the root number. (Multiplication exchange rate) 2 5 8 = 8 5 2

Because 9 5 is a number in the operation? 9 5 has the meaning of 9 times 5, but here it means a number equal to 9 times 5? Personal understanding.

The formula with a root number, the number of squares to be opened is a non-negative number, and the root index is 2 is called a quadratic radical.

<> don't know which situation you want to ask, write both of them, the first one has two solutions, and the next one is simpler.

The horizontal spelling of 2-1/1 is 1 (2-1).

The denominator 2-1 isIrrational numbers, to be carried outThe denominator is rationalized, that is, the numerator and denominator are multiplied by 2-1 at the same timeThere are physical and chemical factors or factors

There are physicochemical factors, factors, for example, the sub-physicochemical factor of 2 is 2, so 1 2= 2 2. And the rational and chemical factor of a+b is a-b, because (a+b)(a-b)=a -b, so the rational and chemical factor of 1 (2-1) is (2+1), and the multiplied denominator becomes 2-1=1, omitted and not written, only 2+1 on the numerator is left - isn't it haha.

I don't know.

You're asking someone.

Find out more and you'll know.

(1) Discriminant formula" 0

i.e. (k-1) +4>0

So k>-3

At the same time, (k-1)>=0, i.e., k>=1

So k is in the range of k>=1

2) The 3-2 integer part is a=1

Then the decimal part is b=3- 2-1=2- 2, and the formula behind the calculation is not clear. But A and B can forget it once they know.

1.It can be seen as a rectangle + 2 equal right triangles.

Because the height is the root number 3 and the waist is 2, the base of the triangle is 1, and the area is the root number of two-thirds.

Therefore, the area of the rectangle is the total area - 2 * the area of the triangle, divided by the height to calculate the upper bottom, the upper bottom + 2 = the lower bottom.

2.Right = (a-1 a) squared, 1 a = (2 + root number three) [2-root number three) (2 + root number three)] = 2 + root number 3

So the original formula = [2 - root number three - (2 + root number three)] square = (-2 * root number 3) square = 12

3.The first half of the question: The left equation is taken apart to get a squared - 4a + 4 + b square - 2b + 1 = 0

(a-2) square + (b-1) square = 0

Because (a-2) squared is greater than or equal to 0, and (b-1) squared is greater than or equal to 0, so a-2=0, b-1=0, so a=2, b=1

Using the idea of the second question, the following is very good, and finally the right equation = (8+5*root number 2) 14

The second half of the question: Let the length of the hypotenuse of the triangle = c, a square + b square = x, then x(x+1) = 12, x*x+x-12 = 0

then (x+4)(x-3)=0, x=-4 or 3

Because x = a square + b squared, obviously greater than or equal to 0, so x = 3, so a square + b square = 3

Obviously, C square = A square + B square, so C = root number 3.

√（3x+2）-√x-8） =3√2

Both sides are the same square.

3x+2-2 (3x+2) (x-8)+x-8=18 is reduced to 2x-12 = (3x+2) (x-8) again squared.

becomes (2x-12) 2=(3x+2)(x-8) and returns to the ordinary quadratic function problem.

x+2 x-1) -x-1 x+2)=5 2 let t= (x+2 x-1), then (x-1 x+2)=1 t is t+1 t=5 2

Multiply t on both sides to get t 2 + 1 = 5 2t

Back to the ordinary quadratic function problem.

I usually eliminate the following sign and use the same yuan or the same square (full square difference is also often used) in the hope that it will help you.

First square both sides at the same time and then open the square, but there are two possibilities to pay attention to when opening the square!

From (root number x + root number y) 2 = (root number 5 - root number 3) 2, x+y = 8-2 times the root number 15-2 times the root number xy, and substitute the root number xy = root number 15 - root number 3 into the above message to drop the root number xy to obtain the root number x + root number y = 8 + 2 times the root number 3-4 times the root number 15

The original formula is equal to.

Under the root number ((3 + root number 5) * (3 - root number 5)).

Under the root number (9-5).

4=2 under the root number

It can be calculated using the perfect square formula.

a-b)*(a+b)=a*a-b*b