I still have quadratic radical exercises in mathematics in the third year of junior high school

1. (1) Two positive roots, that is, x1 is greater than 0, and b 2-4ac is greater than 0, substituting the formula shows that when a is greater than 1, the condition is satisfied!

2) If the condition is satisfied, then x1 times x2 is equal to c a, so a 0, and since b 2-4ac is greater than 0, a 1, and the sum is obtained a 0 satisfies the condition.

Question 1. x^2-2ax+a-4=0

Discriminant formula = 4a 2-4 (a-4) = 4a 2-4a + 16 = 4 (a-1 2) 2 + 15 must be greater than 0

Therefore there must be two different real roots.

By the Vedic theorem.

x1+x2=2a,x1x2=a-4

The equation has two positive roots.

then x1+x2=2a>0,a>0

x1x2>0,a-4>0,a>4

So a>4, the equation has two positive roots.

The equation has two different roots, and the absolute value of the negative root is larger.

then x1+x2=2a>0,a>0

x1x2=a-4<0,a<4

So a<0, the equation has two different roots, and the absolute value of the negative root is larger.

Question 2. Let the root of the equation be x1 and x2, and substitute x1 into the equation to get x1 2-3x1+c=0, that is, c=3x1-x1 2

Equation 2 is x 2 + 3x + x1 2-3x1 = 0

x1'x2'=x1^2-3x1; x1'=-x1;x2'=(x1^2-3x1)/(-x1)=3-x1;

x1'+x2'=-3;That is, (-x1)+3-x1=-3, that is, x1=3, x2=0; So c=x1x2 0

1.△=b^2-4ac

Its 0, there can be no real root.

can be reduced to - x 2-3x+c=0, so you can draw an image of them with an opening up and an opening down, but they have the same focus as the x-axis, i.e., the two equations are symmetrical with respect to the y-axis.

So: c=0

So you can find the root of x 2-3x=0.

Ask for yourself.

From the question "When the drum is filled with water, the water surface in the container drops by 20cm", it can be seen that the volume of water poured out is: 30*30*20 (bottom surface * height) = 18000

The bottom area of the iron drum is 18000 10 = 1800

The side length of the iron bucket is the square root of the bottom area, that is, 1800 open square = 30 and the root number 2 (you will not play the root number).

The volume of water poured into the iron drum in the container v1 = 30 * 30 * 20 is set to be the length of the bottom side of the iron drum is x, and the volume of the iron drum is v2 = 10 * x 2v1 = v2

x = 30 root number 2

Since x-2 0,y +6y+9=(y+3) 2 0, then for the original equation to hold, there must be x-2=0,y +6y+9=(y+3) 2=0

Solve x=2, y=-3, 2x-y=7

a = root number 5 + 2, b = root number 5-2

a+b = root number 5, ab = 5-4 = 1

Root number A 2+B 2+7=(A+B) 2-2AB+7=5-2+7=10

a +b +7 = (root number 5 + 2) + root number 5-2) +7 = 5 + 4 times root number 5 + 5 + 4-4 times root number 5 + 7 = 25 root number 25 = 5 (note ).

It seems that I can't be 100 percent right, but I can guarantee 50 percent right.

I don't know how to use the root number, just say it in words:

Because: the root number cannot be negative.

So, 2-x=x-2=0, i.e. the opposite number is equal to the number and only has the meaning of zero, so x=2

Bring x=2 in, and the left side of the equation=0

So y+1=0, so y=-1

x+y=2-1=1

So x+y=1 under the root number

I hope I understand.

No need to calculate at all!

The definition of the radical formula is: 2-x 0, x-2 0, x=2 substituted into the original formula, y=-1, so: x+y=1

Both 2 x and x 2 make sense, illustrating x=2

Then y = 1, x y is 1.

1.The two right-angled sides of a right-angled triangle are known to be A and BThe hypotenuse is c

1) If a=12, b=5Seek c

2) If a=3, c=4Seek b

3) If c=10, b=9, find a

2.The area of a circle with a known radius of rcm is the sum of the areas of two circles with a radius of 2 cm and 3 cm. Find the value of r.

3.To cut a square with the largest area on a circular steel plate with a radius of 2m, what is the side length of the square? There is one more question.

4.The root number 18-n is an integer. Find the value of the natural number n.

The root number 24n is an integer. Find the minimum value of the positive integer n (1) c = under the root number (144 + 25) = 13

2) b = under the root number (16-9) = root number 7

3) a = under the root number (100-81) = root number 192Pier 2=4 factions 9 factions 13 factions.

r = root number 13

3.The radius of the circle is half the diagonal of the square.

Square side length = 2 root number 2

s = (2 root number 2) 2 = 8

4.(1)n=2\9\14\17

The corresponding results are:

2) n=1, root number 25 is 5

-3 on the left side of the equal-sign spike and then +3: (x-3) + root number (x-3) -6 + 3 = 0 reams root number (x-3) = a

Original formula: a 2 + a - 3 = 0

The number obtained by solving the root equation a is substituted into the root number (x-3)=a.

That's it.

X-3 is converted to a, then x=a+3 is equal to a+3 + root number a and then -6=0 to solve the shift, put the root number on the left side of the equation.

Want to know the answer landline 24418755 I can say it in **.