Brother and sister answer the question of knowing y x 1 2 3x , when x takes what values

When x-1 0 x-1 0

2-3x 0 or 2-3x 0, the value of y is positive.

There is no solution to the first group of inequalities.

Solve the second inequality to obtain: 2 3 x 1

The value of y is positive when 2 3 x 1.

When x-1 0 x-1 0

2-3x 0 or 2-3x 0, the value of y is negative.

Solve the first inequality to get x 1

Solve the second inequality to obtain: x 2 3

The value of y is negative when x 1 or x 2 3.

1] 1 > x > 2/3

2] x > 1 or x < 2 3

Theorem: If b a >0, then ab>0; The reverse is also true.

Answer: 1] For y to be positive, then the product of the numerator and denominator of the fraction must be greater than zero.

That is, (x-1)(2-3x)> 0

Solve the inequality to get 1 > x > 2 3

2] For y to be positive, then the product of the numerator and denominator of the fraction must be less than zero.

That is, (x-1)(2-3x)> 0

Solve the inequality to get x > 1 or x < 2 3

The value of y is positive.

The value of y is negative.

The rest are negative, but don't add 1 and 2 3 to it.

The method is as follows, please comma circle for reference:

If there is help from the landslide, please celebrate.

Known |ⅹ-3|+|x+y|=0 to find the value of -y.

Dear, there is a theme to know, |ⅹ3|AND |x+y|.The sum of the two items is 0, and the absolute value of the buried loss can only be added to 0 after removing the liquid travel, so x=3, y=-3, so x-y=3-(-3)=6.

x^2-2xy+y^2=(x-y)^2

x^2-y^2=(x+y)(x-y)

Pay attention to the decomposition formula, the above two basics, just remember it.

1) From (x+y) =4,, x +2xy+y =4,

From (x-y) =3, x -2xy + y = 3,

, 2(x +y) = 7

So x +y = 7 2

2) - get, 4xy=1, solve xy=1 4

（x+y)²=x²+y²+2xy=4

x-y)²=x²+y²-2xy=3

The above equations are added separately to obtain (1)=

The above equation is subtracted respectively to obtain (2)=

The value of xy is a quarter.

The value of x +y is.

Solution: x+y=4, xy=3

x+y)²=x²+2xy+y²=4=16x-y=√[x-y)²]x²-2xy+y²)√x+y)²-4xy]=√16-4×3)x²-y²=(x-y)(x+y)

Namely. x virtual foci -y = -8 or.

Note: The comrade who said x=3, y=1, have you ever thought about x=1, y=3.

x+y)²=49

So x+y=7 or x+y=-7

x-y)²=1

So x-y=1 or x-y=-1

When x+y=7, x-y=1

So we get x=4 and y=3

When the group returns x+y=7, x-y=-1

So we get x=3 and y=4

When x+y=7, x-y=1

So the solution is to get the fiber or denier x=-3, y=-4

When x+y=7, x-y=1

So the destruction is solved to x=-4, y=-3