Help with this question about the sum of squares. Bonus points!

Knowing a+b=5, b+c=2, find the value of the polynomial a 2 + b 2 + c 2 + ab + bc-ac.

a^2+b^2+c^2+ab+bc-ac)*22a^2+2b^2+2c^2+2ab+2bc-ac(a+b)^2+(b+c)^2+(a-c)^2a^2+b^2+c^2+ab+bc-ac=19

Analysis: From the analysis of the known conditions of the problem, a, b, c cannot find the specific value, so the polynomial should be independent of the specific values of a, b, c, as long as a=5-b, c=2-b into the multinomial number must get a constant.

Solution: a 2 + b 2 + c 2 + ab + bc-ac = b 2-10b + 25 + b 2 + b 2-4b + 4 + 5b b 2 + 2b - (b 2-7b + 10) = 19

Multiply the original by 2 and divide by 2 to become [(a+b) 2+(b+c) 2+(a-c) 2] 2, and finally get 19

I think it's better to give you ideas.

In the first question, the isosceles triangle is used to have equal base angles and two internal angles of parallel lines are equal (e= ead), indicating that AE is the angle bisector of CAE, and the angle divided by the square diagonal (CAD, ACD) is 45°, and the sum of the inner angles of the triangle is 180°

In the second question, using the Pythagorean theorem, the side length of the square is 20 2cm, the diagonal is twice the length of the side (also the Pythagorean theorem), and the area is the square of the side length.

Answer 1:

AC is the diagonal of the square ABCD.

acb=∠acd=45°

ace=135°

ac=ce∠cae=∠cea=(180°-∠ace)/2=(180°-135°)/2=

afc=180°- cae- acd=180°Solution 2:

BC = (EC -EB) = (30 -10) = 20 2 (M) Area of a square ABCD = (20 2) = 800 (M) Diagonal of a square = [(20 2) +20 2) ] = 40 (M).

Because it is a square, ACF=45 and FCE=90

So ace=90+45=135

Because ce=ac

So caf= cef

The sum of the inner angles of the triangle is 180, so cef=(180-135) 2=

So cfe=

So afc=

According to the Pythagorean theorem, BC2=EC2-EB2

So bc = (900-100) = 20 2

So area = (20 2) 2 = 800

Diagonal = ((20 2) 2 + (20 2) 2) (1 2) = 40

1) AC is the diagonal of the square ABCD.

acd=45° ∠dce=90°

ace=∠acd+∠dce=135°

ac=ce ∴∠cea=∠cae=(180°-∠ace)/2=

Again, AFC is an outer angle of the triangle AFC DCE+ CEA 90°+

2) E is the midpoint of AB and EB=10 AB=20 and quadrilateral ABCD is a square Area ABCD=20*20=400 Diagonal AC2=AB2+BC2 AC=20*Root No. 2

∠ead=∠e= ∠d=90° ∴afd= ∴∠afc=180°

Area = Edge Edge = BC BC = 900-100 = 800C

Diagonal AC = BC + AB = 40cm under the root number

Question 1 ACF=45 degrees, FCE=90 degrees, then ACE=135 degreesBecause the triangle ACE is an isosceles triangle, AEC=(180-135) 2=degrees.

So efc=90- aec=degrees.

So afc=180- efc=degrees.

The area of the second question: BC 2=EC 2-EB 2=900-100=800 square meters.

Diagonal 2=2bc 2=1600

Diagonal=40 meters.

1. Because ABCD is a square and AC is a diagonal, the angle ACB = angle ACD = 45 degrees, so the angle ACE is 135 degrees. Because AC=CE, then angular cae=angular AEC=degrees, and because angular ACD+angular afc+angular caf=108 degrees, then angular afc=degrees.

2. From the Pythagorean theorem, BC 2 800, area BC 2 800

Diagonal 2 bc 2 ab 2 1600, diagonal 40

For the first question, I need a diagram;

In the second question, according to the Pythagorean theorem, calculate the length of the hypotenuse of the first triangle is 13cm, and then calculate the height on the hypotenuse of the first triangle according to the equality of the area, which is 12*5 13, according to the theorem of similar triangles, the ratio of the opposite sides is equal, 13 to 20 is equal to 12*5 13 to x, then x is the height of the hypotenuse of the second triangle.

According to the Pythagorean theorem, the hypotenuse of the first triangle can be calculated as 13, and then the height can be calculated as 60 13 by using the area

And because they are similar (i.e., similar triangles).

It is possible to get the height of another triangle.

According to the Pythagorean theorem, calculate the length of the hypotenuse of the first triangle is 13cm, and then calculate the height on the hypotenuse of the first triangle according to the equality of the area, which is 12*5 13, according to the theorem of similar triangles, the ratio of the opposite sides is equal, 13 to 20 is equal to 12*5 13 to x, then x is the height of the hypotenuse of the second triangle

Let the trimmed triangle be cut to an edge length of x

So 2-2x = under the root number (square of x + square of x) to solve x=?

Then the side length of the octagon = under the root number (square of x + square of x) = 2-2xx=

Then the side length =

That is, the side length of the bar square is divided into three equal parts, and one of them is the side length of the octagon.

So the total side length of the octagon is.

Solution: 1).

Take the midpoint o of de and connect ao

Because: ad bc, af bc

So: af ad

So: dae=90°, ao is the midline on the rt dae hypotenuse de so: ao=do=eo=de 2=ab

So: abo= aob=2 ado

Because: ad bc, ado= ebf

So: abo=2 ebf

Because: abc= abo+ ebf=3 ebf=75° solution: ebf=25°

So: ade= ado= ebf=25°So: ade=25°

2) Because: ade+ aed=90°

So: aed=65°

The length of the three sides x+y+z=36,x+y=2z,x-y=z 3x+y+z=851,x*,y*

Number of people per room and number of beds missing Total number of people and number of rooms, 7x+3=y, 8x-5=yx-y=3,100x+10y+z 100y+10x+z

Classmates, you have time to type so many words, why don't you use your brains to do it yourself!

Why bother?

Brain-dead, brain-dead, such a simple thing still needs to be asked. If you don't teach, it's your father's fault; If the teaching is not strict, the teacher is lazy.

=2π/3

The modularities of a, b, c, and a+b are equal.

The modulus of A+B = the two ends of the front pressure after the translation of A or B are connected from end to end to form an equilateral triangle, and the angle before translation is complementary to the angle of the triangle.

So the angle between a and b=π-π/3