Does anyone know how to solve x 2x 3 0?

Let y= +2 -3=0, then.

1) ( 3) = 0, -1 = 0 or x + 3 = 0, x = -3 or x = 1, y = +2 -3 is the parabola with the opening pointing upward.

There are two intersections with the x-axis (-3,0), (1,0), to make y 0, take the middle, i.e., -3 1, and the result is written as a set:

The diagram is as follows: <>

x2+2x-3≤0

i.e. (x+3)(x-1) 0

i.e. x+3 0 and x-1 0 or x+3 0 and x-1 0 i.e. -3 x 1 or no solution.

So -3 x 1

In this problem, we will first use the cross multiplication method to decompose the unary quadratic polynomial on the left.

If we first observe that the coefficient of the primary term of x is 2, then we can split -3 into the product of 3 and -1, so that 3+(-1) is exactly equal to 2.

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

Solution: -3 x 1

The equation before this unequal sign can be multiplied by the cross to (x-1) and multiplied by (x+3), and according to the image of the quadratic function, his result should be greater than or equal to -3 and less than or equal to 1

Factorization. x-1)(x+3)≤0

3 x 1, i.e. what you want.

x²+2x-3≦0

x+1）²-2²≦0

x+1+2）×（x+1-2）≦0

x+3）×（x-1）≦0

When x+3 0, x-3

When x-1 0, x 1

So the solution to x is, x 1

Solution: x +2 -3 0

x+3)(x-1) 0,got.

x+3≤0，x-1≤0

x1≤-3，x2≤1

The solution of the original inequality is:

x≤-3

The left side of the inequality is decomposed to (x+1)(x-3) 0 by cross multiplication, so the solution set is -1 x 3.

How to solve 2x x 0 is as follows:

x(2－x)=0

x=0 or 2 x=0

Solution x = 0 or 2

x（2-x）=0

Solution x = 0 or 2

So, solve the equation and get x=0 or 2.

Shift, the original formula is x 2 + x-2 = 0, after cross multiplication, the original formula is (x + 2) (x-1) = 0, x1 = -2, x2 = 1

Solution: x |x-2|=x

x²|x-2|-x=0

x(x|x-2|-1)=0

x=0 or x|x-2|-1=0

x|x-2|-1=0

When x<2, x(2-x)-1=0, x-2x+1=0, x-1) =0, x=1;

When x 2, x(x-2)-1=0, x-2x-1=0, x=1+2 or x=1-2 (rounded).

So the solution of the original equation is x1=0, x2=1, x3=1+ 2

x^2.|ⅹ2|=ⅹ

Extract the common factor x

x(x|x-2|-1)=0

Derived. x=0 or x|x-2|-1 =0

It should be considered on a case-by-case basis.

case 1: x<2

x|x-2|-1 =0

x(x-2)-1 =0

x^2-2x+1 =0

x-1)^2=0

x=1case 1: rounded.

case 2: x≥2

x|x-2|-1 =0

x(x-2)-1 =0

x^2-2x-1=0

x=1+√2 or 1-√2

solution for case 2: x=1+√2x^2.|ⅹ2|= Solve.

x=0 or 1+ 2

Answer: x -2x-3 = 0

Solution 1: Formula method.

x=[-b±√(b²-4ac)]/(2a)=[2±√(4+12)]/2

x1=-1，x2=3

Solution 2: Cross multiplication.

x 1x -3

The equation is decomposed into (x+1)(x-3)=0

So: x+1=0 or x-3=0

So: x1=-1, x2=3

Solution 3: Factorization.

x²-2x-3=0

x²-1-2x-2=0

x-1)(x+1)-2(x+1)=0

x+1)(x-1-2)=0

x+1)(x-3)=0

x1=-1，x2=3

One root of the equation x + (k-1) x-3 = 0 is 1, so what is the value of k? What is the other root?

x1 = 1, and the other root is x2

According to Veda's theorem:

x1+x2=1-k

x1*x2=-3

x1=1 substitution:

1+x2=1-k

x2=-3 gives k=3 and the other root is -3

2x²+5x-1=0

This equation is the fastest to solve using the formula method:

x=[-b±√(b²-4ac)]/(2a)=[-5±√(25+8)]/(2*2)

At first glance, it is easy to ask online, what can you learn, these questions are good for the basics.

2x-x 0 deformation.

x²-2x≤0

Defactoring.

x（x-2）≤0

So 0 x 2

2x2-x+1>0

i.e. (2x+1)(x-1)>0

So 2x+1>0 and x-1>0

or 2x+1<0 and x-1<0

i.e. x>1 or x<

Because =(-1) 2-4 2 1=-7 0

Therefore, the parabolic function has no intersection point with the x-axis, that is, the parabolic function images are all above x=0.

So the set of solutions of this inequality is: x belongs to r.