Given: x-xy = 40, xy-y = - 20, finding: x + y =? Is a problem in grade one of junior high school,

Given: x-xy = 40, xy-y = - 20, finding: x + y =? Is a problem in grade one of junior high school,

X-xy = 40 (1) xy-y = - 20 (2) (1) + (2) get: x-xy + xy-y = 40-20 = 20, that is, X-Y = 20, then: (X-Y) ^ 2 = (x + y) ^ 2-4xy = 400 (1) - (2) get: x-xy-xy + y = 40 - (- 20) = 60, that is, x + y-2xy = 60, let x + y = a, xy = B, then a ^ 2-4b = 400, a-2b = 60, known equations can be solved (very difficult to calculate, calculate by yourself

Find the real number solution of the system of equations, 5 (x + 1 / x) = 12 (y + 1 / y) = 13 (Z + 1 / z), XY + YZ + ZX = 1. Hint: you can use trigonometric substitution or dead calculation

Find the real number solution 5 (x + 1 / x) = 12 (y + 1 / y) = 13 (Z + 1 / z), XY + YZ + ZX = 1, from XY + YZ + ZX = 1, get 1 / x + 1 / y + 1 / z = 1 / XYZ. (1) from (1 / x + 1 / y + 1 / z) & sup2; = 1 / X & sup2; + 1 / Y & sup2; + 1 / Z & sup2; + 2 (1 / XY + 1 / YZ + 1 / ZX) = 1 / X & sup2; + 1 / Y & sup2; + 1 / Z & sup2; + 2 (x + y + Z) / XY

It is known that nonzero vector AB and vector AC satisfy (vector AB divided by / vector AB / + vector AC divided by / vector AC /)*
If vector BC = 0 and (vector AB divided by / vector AB) * (vector AC divided by / vector AC /) = 1 / 2, then why is triangle ABC a triangle?

The vector AB and the vector AC satisfy (the vector AB is more than the vector AB's friction + the vector AC is more than the vector AC's friction) * the vector BC = 0. It is known that the sum of the unit vectors on the edge of AB and AC is perpendicular to BC. According to the parallelogram rule of vector addition, the sum of the two unit vectors is perpendicular to their difference and equally divided, so it is proportional to the line segment of the parallel line

In the known triangle ABC, AC = root 6, BC = 2, B = 60 °, find C

From the sine theorem, we get
AC/sinB=BC/sinA
Root 6 / sin 60 ° = 2 / sin a
sinA=√2/2
therefore
A = 45 ° (135 ° rounded off)
thus
∠C=180°-60°-45°=75°

F (x) = logax (a > 0, a is unequal to 1), sequence 2, f (A1)... F (an), 2n + 4 are arithmetic sequence, find the general term of an

A is too much, change a m, f (x) = logmx (M > 0, M is not equal to 1), sequence 2, f (A1)... F (an), 2n + 4 are arithmetic sequence, find the general term of an, let B1 = 2, B2 = f (A1) ,b(n+1)=f(an),b(n+2)=2n+4,bn=2+(n-1)db(n+2)=2+(n+1)d=2n+4(n+1)d=2n+2d=2bn=2+2(n-1)=nb(n+1)=f(an)=l...

How to prove that four points are coplanar

Take any two of them as vectors and take the other two as vectors to prove that two vectors are parallel or intersect

In the triangle ABC, where AB is greater than AC, the intersection of angle FBC = angle ECB = 1 / 2, angle a, CE, BF and points m, e, f are on AB, AC respectively. Prove be = CF

Extend me to p to make MP = MF
∵∠FBC=∠ECB=x
∴△PMB≌△FMC
∵∠FMC=2x=∠BAC
∴∠AEC=∠MFC=∠PEB=∠MPB
∴PB=EB
∵PB=FC
∴BE=CF
Are you from Hangzhou inter!

Don't worry about the equation
1. The average score of Xiaoying's six subjects in the midterm exam is 80 points. After adding mathematics, the average score is 2 points more. How many points did Xiaoying get in the math exam this time?
2. Xiao Wang rides from point a to point B at the speed of 24 km / h, and returns to point a from point B at the speed of 16 km / h to find the average speed of Xiao Wang
3. A, B and C paid the same amount of money to buy the same number of pens. After they bought them, both a and C were three less than B. therefore, B gave a and C 1.5 yuan respectively. What is the unit price of pens?
4. For a two digit number, the sum of the number on the tenth digit is 11 when it is doubled. If the number on the tenth digit is multiplied by five times and the sum is 17, the two digit number can be obtained
5. There is a grade in a primary school. Two classes (Class A and class B) in each grade give 3000 bread to six grades. There are 600 bread left. It is known that class A and class B in each grade get 100 more bread. How many bread do class A and class B in each grade get
6. Xiao Wei and Xiao Ming have 128 yuan in total. After Xiao Wei gives Xiao Ming 6 yuan, Xiao Wei has 4 yuan more than Xiao Ming. How much did Xiao Wei and Xiao Ming have?

1. After adding mathematics, the average score is: 80 + 2 = 82 points, mathematics: 82 × (6 + 1) - 80 × 6 = 94 points, or directly use: 2 × 7 + 80 = 94 points. 2. Any distance can be set, for the convenience of calculation, set ab distance as 48 km, and the average speed of round-trip is 48 × 2 ^ (48 ^ 24 + 48 ^ 16) = 96 ^ 5 = 19.2 km or

What is the unit vector parallel to the vector a = (12,5)? Why? Especially how to think about such a problem? What are the characteristics of the unit vector parallel to a vector?

Such a question is to test the unit vector, parallel unit vector is divided into two kinds, in the same direction and reverse
But the solution of the unit vector is very fixed, that is, the vector divided by its own module, so the length of the vector becomes 1, so it becomes the unit vector
① The unit vector in the same direction as vector a is a / | a | = (12,5) / √ (12 & # 178; + 5 & # 178;) = (12 / 13,5 / 13)
② The unit vector opposite to vector a is - A / | a | = - (12,5) / √ (12 & # 178; + 5 & # 178;) = (- 12 / 13, - 5 / 13)

(1) As shown in Fig. 1, the bisector AE of ∠ bad intersects with the bisector ce of ∠ BCD at point E, ab ‖ CD, ∠ ADC = 40 ° and ∠ ABC = 30 ° to calculate the size of ∠ AEC; (2) as shown in Fig. 2, the bisector AE of ∠ bad intersects with the bisector ce of ∠ BCD at point E, ∠ ADC = m ° and ∠ ABC = n ° to calculate the size of ∠ AEC; (3) as shown in Fig. 3, the bisector AE of ∠ bad intersects with the bisector ce of ∠ BCD at point E, then the bisector AE and ∠ ADC Is there still some equivalent relationship between ABC and ABC? If there is, please write your conclusion and give proof; if not, please give reasons

(1) ∵ CE bisection ∠ BCD, ∵ AE bisection ∠ bad ∵ ECD = ∠ ECB = 12 ∠ BCD, ∵ ead = ∠ EAB = 12 ∠ bad, ∵ D + ∵ ECD = ∠ e + ∵ ead, ∵ B + ? EAB = ∠ e + ∵ ECB, ∵ D + ∵ ECD + ∵ B + ∵ EAB = ∠ e + ∵ ECB + ∵ B + ∵ EAB = 2 ∵ e, ? e = 12 (∠ D + ∵ b), ?