What is the x 3 x 1 0 solution

Solution: From: x 3+x-1=0, divide x by x on both sides of the equation to get x 2+1-1 x=0

That is: x 2 + 1 = 1 x

Their intersection is in the first quadrant.

When x = 1, y = x 2 + 1 = 2, y = 1 x = 1, at this time parabola.

The image is in an inverse proportional function.

Above; When x=1 2, y=x 2+1=5 4, y=1 x =2, the image of the inverse proportional function is above the parabola.

The real root x of the equation x 3 + x -1 = 0 is in the range of 1 2 x 1

Xie Qiwei: x=3 or x=-1. This is a one-dimensional equation, and there is a formula method for solving common seepage bending.

Matching method, factorization method.

The problem is that the two numbers are multiplied to equal to 0, so as long as any one of them is equal to 0, so let -3=0 solve x=3, let +1=0 solve and shout pei x=-1

Solution: The original equation is converted into two one-branch one-branch one-dimensional equations x-3=0 or x+1=0, and then the first-time equation can be solved after the radical is violently disturbed

Question Analysis: (x-3)(x+1)=0

then x-3 = 0 or x+1 = 0

x=3 or x=-1

x+1=0 or x-3=0

x = -1 or slag and x = 3

x-3)(x+1)=0

x(x+1)-3(x+1)=0

x^2+x-3x-3=0

x^2-2x=3

x^2-2x+1^2=3+1^2

x-1)^2=4

x-1 = +2 or -2

x-1=2 or Qiliang with high reed x-1=-2

x=3 or x=-1

Summary. Answer-1, the solution of the equation x=-1, solution: 3x(x+1)=0, x+1=0, x=0-1, x=-1, the solution of the equation is x=-1, and zero multiplied by any number is equal to zero.

3x(x+1)=0.

Answer: Sun Jing's case-1, the solution of the equation x=-1, the first Kai solution: 3x(x+1)=0, x+1=0, x=0-1, x=-1, the solution of the square cooker is x=-1, zero multiplied by any number is equal to zero.

Answer: Sun Jing's case-1, the solution of the equation x=-1, the first Kai solution: 3x(x+1)=0, x+1=0, x=0-1, x=-1, the solution of the square cooker is x=-1, zero multiplied by any number is equal to zero.

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How to solve it with the matching method.

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First, let 3x(x-1)=0 solve x.

x=0 or x=1.

Because the image is open upwards.

So when x<0 or x>1, the function y is greater than the bending rent 0; When the solution of 0 is x<0 or x>1.

That is, the final answer is x<0 or x>1.

Solution:1When x 0, x-1 0 x 1

The two inequalities are combined to give x 1

2.When x<0, x-1<0 x 1

The two inequalities are combined to give x<0

So the solution set of this original cavity inequality is: x 1 or x 0 pro, your is the greatest support of the annihilation chain to my round book, I wish you a pleasant time.

It is discussed in three situations, including 1When the wheel is combined with x<0, 3x<0, x-1<0, 3x(x-1)>0, the inequality holds; 2.When 00,x-1<0,3x(x-1)<0, the original inequality does not hold; 3.

When x>1, 3x>0, x-1>0, 3x(x-1)> Lasan 0, the inequality holds.

So, x<0 or x>1

Let f(x)=|x-1|-|x-3|

When x 1, f(x)=-x+1+x-3=-2, and f(x) 0

At 1 x 3, f(x)=x-1+x-3=2x-4 at this time f(x) 0, and the solution is 2 x 3

When x 3, f(x)=x-1-x+3=2

At this point f(x) 0

To sum up,|x-1|-|x-3|The solution of >=0 is x 2

Summary. The solution of an inequality is the value of an unknown number that makes the inequality true in an inequality that contains unknowns. The solution of inequality is one of the basic concepts of inequality, which refers to the value of the unknown number that can make the inequality true in an inequality containing unknowns, and the whole solution of the inequality is called the solution set of the inequality, sometimes referred to as the solution.

<>x-1) (3-x)>0.

The answer is 1 x 3

Classmates, let's draw pictures faster for this kind of problem.

Steps to solve the inequality: <>

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2. Remove brackets; 3. Selling and merging similar items; 4. The coefficient is turned into a post-cluster comic to solve the wheel let.

The solution of the unequal basis is the value of the unknown number that can make the inequality hold in the inequality that contains unknowns. The solution of inequality is one of the basic concepts of inequality Pisan, which refers to the value of the unknown number that can make the inequality hold in an inequality containing unknowns, and the whole solution of the inequality is called the solution set of the inequality, sometimes referred to as the solution. <>

x^2-3x+1=0

x1 = (pure limb 3 + root tan pants clear number 5) let the first 2

x2 = (3 - root number 5) 2

Solution: From: x 3+x-1=0, divide x by x on both sides of the equation to get x 2+1-1 x=0

That is: x 2 + 1 = 1 x

Their intersection is in the first quadrant.

When x=1, y=x 2+1=2, y=1 x=1, the parabolic image is above the inverse proportional function;

When x=1 2

, y=x 2+1=5 4

y=1 x2, where the image of the inverse proportional function is above the parabola.

The real root x of the equation x 3 + x -1 = 0 is in the range of 1 2 x 1

△=9+4=13

x=（-3±√13）/2

Your likes or adoptives are what motivate me to continue helping others.

Using the root finding formula, x = 2 parts (-3 plus minus 13 under the positive and negative root signs).

What is the solution of x 2 + 3 x - 1 = 0 from?

Solution: x bai2+3x-1=0

Method 1: Matching DU Method:

x^2+3x-1=0

x 2+3x+(3 2) 2-(3 2) 2-1=0(x+3 2) 2=13 4= ( 13 2) 2 then x+3 2=

zhi13/2

x=-3/2±√13/2

Method 2: Formulas.

DAO method: x=(-3 (3 2+1*4)) 2

x²+3x+1=0

x²+3x++9/4-9/4+1=0

x+3/2）²=9/4-1

x+3/2）²=5/4

x+3/2=±√5/2

x₁=√5/2-3/2=（√5-3）/2

x₂=-√5/2-3/2=（-√5-3）/2Additional Information:

The matching method is connected to the general flow of a quadratic equation

1. It is transformed into a general form, that is, the form of ax +bx=c=0.

2. Convert the quadratic term coefficient to 1.

3. Move the constant term to the right of the equal sign, that is, move the term.

4. Add half of the square of the primary term coefficient to both sides at the same time, and form a perfect square formula.

5. Open squared.

6. Calculate the value of x.

For example, 3x = 3-8x

Divide both sides by 3 to get: x +8 3x-1=0 to get x +8 3x=1

Add (4 3) to both sides at the same time to get :x +8 3x+ (4 3) =1+(4 3).

Recipe: (x+4 3) =25 9

Open squared: x+4 3= 5 3

i.e.: x+4 3=5 3 or x+4 3=-5 3x =1 3

x₂=-3