Question

POMOOOOOCY !!!!!!

Rozwiąż równania :

a) (2x - 5)² + 11x + 2 = (2x +3 )(2x-3)

b) ( ½ x -2)² - 3 = ( ½ x - 4)(0,5 x +4)

c)( 2 - √2 ) ( x + √2) = 6 - √2

d) 3 - √3x = x -1

e) √2(x - 3) = x+4

Answer 1

a]

(2x-5)²+11x+2=(2x+3)(2x-3)

4x²-20x+25+11x+2=4x²-9

4x²-4x²-9x+25+9=0

-9x=-34

x=34/9

x=3 ⁷/₉

b]

(½x-2)²-3=(½x-4)(0,5x+4)

¼x²-2x+4-3=¼x²-16

¼x²-¼x²-2x=-16-1

-2x=-17

x=17/2

x=8,5

c]

(2-√2)(x+√2)=6-√2

2x+2√2-x√2-2=6-√2

2x-x√2=6-√2+2-2√2

x(2-√2)=8-3√2

x=(8-3√2)/(2-√2)

x=[16+8√2-6√2-6]/[ 4-2]

x=[10+2√2]/2

x=2(5+√2)/2

x=5+√2

d]

3-√3 x=x-1

3+1=x+√3 x

x(1+√3)=4

x=4/(1+√3)

x=[4-4√3]/[1-3]

x=-2(2√3-2)/-2

x=2√3-2

e]

√2(x-3)=x+4

√2x-3√2=x+4

√2x-x=4+3√2

x(√2-1)=4+3√2

x=(4+3√2)/(√2-1)

x=4√2+4+6+3√2

x=7√2+10

Answer 2

a) (2x - 5)² + 11x + 2 = (2x +3 )(2x-3)

4x²-20x+25+11x+2=4x²-9
-9x=18

x=-2

 

b) ( ½ x -2)² - 3 = ( ½ x - 4)(0,5 x +4)

¼x²-2x+4-3=¼x²-16

-2x=-17

x=17/2

c)( 2 - √2 ) ( x + √2) = 6 - √2

2x+2√2-x√2-2=6-√2

2x-x√2=8-3√2

x(2-√2)=8-3√2 

x=(8-3√2)/(2-√2)

x=(8-3√2)/(2-√2) * (2+√2)/(2+√2) = (16 +8√2-6√2-6)/(4-2) = (10-2√2)/2 = 2(5+√2)/2 = 5+√2  nawiasy to ulamki zwykle, mysle ze sie polapiesz

x=5+√2

 

d) 3 - √3x = x -1

3+1=x+√3x

x+√3x=4

x(1+√3)=4

x= 4/(1+√3) = 4/(1+√3) * (1-√3)/(1-√3) = (4-4√3)/(1-3) = (4-4√3)/-2 = -2(-2+2√3)/(-2)=-2+2√3

x=-2+2√3

 

e) √2(x - 3) = x+4

x√2-3√2=x+4

x√2-x=4+3√2

x(√2-1)=4+3√2

x=(4+3√2)/(√2-1) = (4+3√2)/(√2-1) * (√2+1)/(√2+1) = (4√2+4+6+3√2)/(2-1) = (7√2+10)/1 = 7√2+10

x=7√2+10