Mathematics Mathematics Perfect Square Formula, Mathematics Mathematics Perfect Squared Formula

x+y)²=49

x²+2xy+y²=49

2xy=49-25=24

x-y) =x +y -2xy=25-24=1x-y=1 or -1

And because x>y, take 1

Hope it helps.

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The perfect squared formula is an important knowledge base for algebraic operations and deformations.

Focus: It is the memorization and application of the perfect square formula

Difficulty: It is the understanding of the characteristics of the formula (such as the understanding of the coefficient of the primary term of the product in the formula).

1. Understand the left and right features of the formula.

1) Learn to derive formulas (these two formulas are obtained according to the meaning of the power and the multiplication rule of polynomials), and truly experience the incorrectness of arbitrary "creation";

2) Learn to summarize the meaning of formulas in words:

The sum (or difference) of two numbers is squared, equal to their sum of squares, plus (or subtracted) 2 times their product and is called the perfect square formula For the sake of distinction, we call the former the perfect square formula of the sum of two numbers, and the latter the perfect square formula of the difference between two numbers

c) The structural features of these two formulas are:

1. The left side is the multiplication of two identical binomials, and the right side is the trinomial, which is the sum of the squares of the two terms in the left binomial, plus or minus 2 times the product of these two terms; 2. When the two symbols on the left are the same, the items on the right are all connected with the " " sign; When the two symbols on the left are opposite, the square term on the right is connected by the " " sign and then twice the product of the two terms " (note: the symbol is not included when the term is said here);

3. The letters in the formula can represent specific numbers (positive or negative), or they can represent mathematical formulas such as monomials or polynomials

d) Unity of the two formulas:

Because the two formulas can actually be seen as one formula: the perfect square formula for the sum of two numbers. This prevents confusion of formulas and errors in the operation symbols. （2

Expression: (a+b)(a-b)=a 2-b 2, the product of the sum of the two numbers and the difference between the two numbers is equal to the square difference of the two numbers, and this formula is called the formula for the difference of square.

When the division is the sum of two numbers and the difference between the two numbers is multiplied, the product is binomial. This is because when two binomials with such characteristics are multiplied, two terms of the product will appear that are opposites of each other, and the result of combining these two terms will be zero, so that there will be two left. And their product is equal to the square difference of these two numbers in the multiplication, i.e., (a+b)(a-b)=a 2-b 2, and the product of the sum of the two numbers and the difference between these two numbers is their square difference.

Completely bai

The square du formula zhi: (a+b) = a +2ab+b (a+b) = a -2ab+b

The squared DAO difference formula is: (a+b)(a-b)=a -b

Expression: come(a+b)(a-b)=a 2-b 2, the product of the sum of the two numbers and the difference between the two numbers of the source is equal to the square difference of the two numbers, and this formula is called the square difference formula of multiplication.

1.Because 1 of a + a = 3, therefore, dua + a is equal to 1 of zhi3, so a is equal to 6 parts of dao1, so you can calculate a + a square of the four times of the answer of a + a + a of the fourth power of the square is equal to your own calculation.

2.If b is equal to 2 times the root 5, then a can be calculated

The square of the du zhi one = (a + a part one) dao -2 a a a part of the return 1 = (a + a part one.

A) squared -2

1/1 of a+a = 3

So a + a part of the square = (a + a part of the square) - 2 = 7 squared - 2 = 47

Because a to the fourth power + a to the fourth power = (a + a square part) -2 a a square = (a + a square part) -2 a a square part - (a + a square part) -2 = 47 -2 = 2207

2.Because a +b = (a-b) +2ab

So a +b = 2 +2 1 = 6

And 47 years of wood have seen.

The answer to the first question is:

The answer to the second question is 6

1. Known.

Source a+1 a=3, find a bai2+1 a du2 =? and a zhi4+1 a 4 =?

Answer: (daoa+1 a) 2=9 a 2+2+ 1 a 2 =9 a 2+1 a 2 =7

And so on: (a 2+1 a 2 ) 2=49 a 4+1 a 4 +2=49 a 4+1 a 4 =47

2. Knowing a-b=2, a b=1, find the value of a + b.

a-b) 2=4 a +b -2ab=4 because ab=1 so a +b =6

A square + B square = (a + b) square - 2ab = 2 square - 2 times 1 = 2

1.Several times square, the first 2nd and 4th power, respectively.

2 1 out of a = 3 then a = 1 out of 6 and everything else can be calculated.

a-b square = 4, so a square plus b square = a-b square -2ab = 2

1. Knowing a+1 a=3, find a2+1 a2=? and a 4+1 a 4 =?

Answer: (a+1 a) 2=9 a 2+2+ 1 a 2 =9 a 2+1 a 2 =7

And so on: (a 2+1 a 2 ) 2=49 a 4+1 a 4 +2=49 a 4+1 a 4 =47

2. Knowing a-b=2, a b=1, find the value of a + b.

a-b) 2=4 a +b -2ab=4 because ab=1 so a +b =6

It's actually very simple, take some time to study hard.

Answer: 7; 47；6

I don't know how to type out the process.

1.(a+1/a)(a+1/a）=a2+1/a2+2=3*3。The same goes for the fourth power.

2.(a-b)2=a2+b2-2ab=4 and ab=1 is known, then 2ab=2 can be brought in again.

For the first question, the answer to the first question is 7, and the answer to the second question is 47

The second question, the answer is 2

Wrong Your first question is very nb

Because dua+1 a=3, a zhi2+2*a*1 a+1 a 2=9 a 2+1 a 2=7

In the same way, a 4+1 a 4=47

Because daoa-b=2 so a 2-2ab+b 2=4 2ab=2 so a 2+b 2=6

Wrong, wrong, it should be two values of 18 or -18

x + kx + 81 is a perfectly flat way.

The perfect square formula is a 2ab+b, x +kx+81 where a is x, b =81, so b=9, so 2ab=18x, so k=18, but there is also a -2ab, so it should be two results.

i.e. k = 18

k=±18；

Process: x 2 2 * 9 * x + 9 2;

According to (a b) 2=a 2 2ab + b 2;

b^2=81；

Therefore: b=9 or b=-9;

Therefore: k=18 or k=-18;

I hope it helps!! 1

Faint has already been adopted! All right.

Perfect flat discriminant = k 2-4 * 81 = 0

k=+-18

The answer is plus or minus 18, two answers.

It's simple, just a formula.

a+b)^2=a^2+2*a*b+b^2=x²+kx+9²

k =18

k=18。The formula is (x+z) 2, where z is an unknown number, and we get x 2+2xz+z 2, where z 2=81, so the solution is z=9, so k=2z=18

By the perfect square formula, (a+b) 2=a2+2ab+b2, so 81 is equal to b2, both b=9, so k is equal to 2b is equal to 18

All the time x 2-xy=3, xy-y 2=-6, then the value of x-y is 3

x^2-xy -xy+y^2=9

x-y）²=9

x-y=±3

If |x+3|+4y 2+4y+1=0, then the value of y x is -8 x+3|+（2y+1）²=0

x+3=0，2y+1=0

x=-3，y=-1／2

Knowing that ax 2-12x+1 is a perfectly squared formula, then a = 6

ax^2-2×6x×1+1

6x-1）²

If a+b=3, then the value of 2a2+4ab+2b 2-6 is 12

a+b=3（a+b）²=3²

2（a^2+2ab+b^2）-6

2（a+b）²-6

1. ±3

It's simple, do the math yourself! Use your brains to get a reward!

Solution: 1. Because x 2-xy=3, xy-y 2=-6, the two equations are subtracted to obtain, x 2-xy- xy+y 2=3+6

i.e. (x-y) 2=9, so x-y= 3

2、|x+3|+4y 2+4y+1=0 is |x+3|+(2y+1) 2=0, the non-negative sum is 0, each 0, x+3=0, 2y+1=0, then, x=-3, y=-1 2

y^x=(-1/2)^-3=(-2)^3=-8

3. Knowing that ax 2-12x+1 is a perfectly squared formula, then (6x) 2-12x+1 is a perfectly squared formula, a= 6

a^2+4ab+2b^2-6=2（a^2+2ab+b^2）-6=2（a+b)^2-6=2x3^2-6=18-6=12

1、x^2-xy=x（x-y）=3，① xy-y^2=y（x-y）=-6 ②

, get (x-y) =9

x-y = 3 or -3

2、|x+3|+4y^2+4y+1=0

x+3|+(2y+1) 2=0, the sum of non-negative numbers is 0, each is 0, x+3=0, 2y+1=0, then, x=-3, y=-1 2y x=(-1 2) -3=(-2) 3=-83, knowing that ax 2-12x+1 is a perfectly squared formula, then (6x) 2-12x+1 is a perfectly squared formula, a= 6

a^2+4ab+2b^2-6

2（a^2+2ab+b^2）-6

2（a+b)^2-6=2x3^2-6

a+b)2=a2+2ab+b2.

a-b)2=a2-2ab+b2Common errors.

Common mistakes in the perfect squared formula are:

An item was missed.

Confuse the formula. Symbol error in calculating limb missing fruit.

Variant applications are difficult to master.

a+b)2=a2+2ab+b2.

a-b)2=a2-2ab+b2

The above two formulas can be combined into one formula: (a b)2=a2 2ab+b2(Note: the rear demolition surface must be a plus sign).

Morph application. Known A+

Calendar Imperial Debate 2(a+b)^2=(a-b)^2+4ab3.(a-b) 2=(a+b) 2-4ab This paragraph is completely squared and the formula is misunderstood.

The perfect square formula can be represented by letters as a 2+2ab+b 2=(a+b) 2 and a 2-2ab+b 2=(a-b) 2

Junior high school math wax dress wheel key stove perfect square public bright mode:

a+b)^2=a^2+2ab+b^2；

a-b)^2=a^2-2ab+b^2