Question

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|3x + 3| = 6
|x + 3| -2x = 9

|x² - 16| = 7

 

Решить иррациональных уравнений

√x+10 = 2
√4x+1 = 2x-1

√36x²-12x+1    +3x = 4

Answer 1

|3x + 3| = 6

1) x>0           2)x<0

3x+3=6        -(3x+3)=6

3x=3              -3x-3=6

x=1                 -3x=9

                        x=-3

========================  

|x + 3| -2x = 9

1)x>0             2)x<0

x+3-2x=9         -(x+3)-2x=9

-x=6                   -x-3-2x=9

x=-6                   -3x=12

                             x=-4

========================

|x² - 16| = 7

1)x>0                2) x<0

x^2-16=7         -x^2+16=7

x^2=25               -x^2=-9

x=-5 и x=+5          x^2=9

                                 x= +3  и x=-3

 

 

 √x+10 = 2

возведем в квадрат

√(x+10)^2=2^2

x+10=4

x=-6

 

 √4x+1 = 2x-1

√(4x+1)^2=(2x-1)^2

4x+1=4x^2-4x+1

-4x^2+4x+4x+1-1=0

-4x^2+8x=0

4x^2-8x=0

4x(x-2)=0

4x=0    илм x-2=0

x=0                x=2

 

√36x²-12x+1    +3x = 4

√(36x^2-12x+1)^2=(4-3x)^2

36x^2-12x+1=16-24x+9x^2

36x^2-9x^2-12x+24x+1-16=0

27x^2+12x-15=0   :3

9x^2+4x-5=0

д=16+4*9*5=196=14^2

x=(-4+-14)/18= -1:   1018= 56