Question

Prosze o rozwiązanie 2.75

Answer 1

a) (x + 3)^2 = (2x - 1)^2

x ^ 2 + 6x + 9 = 4x^2 - 4x + 1

-3x^2 + 10x + 8 = 0

Δ = b^2 - 4ac

Δ = 10 ^ 2 + 4 * 3 * 8 = 196

√Δ = 14

 

x1 = 4

x2 = -2/3

 

b) (3 - 4x) ^2 = (5x - 2)^2

9 - 24 x + 16x ^2 = 25x^2 - 20 x + 4

-9x^2 -4x + 5 = 0

Δ = 196

√Δ = 14

x1 = -1

x2 = 10/18 = 5/9

 

c) (2x - 1)^2 = (3x +4)(x - 3) + 19

4x^2 - 4x + 1 = 3x^2 - 9x + 4x - 12 + 19

x^2 +x - 6 = 0

Δ = 25

√Δ = 5

x1 = -3

x2 = -2

 

d)(x - 4)^2 = (2x - 3)(x + 1) + 1

x^2 - 8x + 16 = 2x^2 + 2x - 3x - 3 + 1

-x^2 -7x +18 = 0

Δ = 121

√Δ = 11

x1 = -6

x2 = 2

 

e)(3x - 2)(x + 1) = (2x -3)(x + 2)

3x^2 + 3x - 2x -2 = 2x^2 + 4x - 3x - 6

x^2 + 4 = 0

Δ =-16

równanie sprzeczne - brak rowiązań

 

f) (3x -2) ^2 -5(2x + 3) = (2x - 3)^2

9x^2 - 12x + 4 - 10x -15 = 4x^2 - 12x + 9

5x^2 - 10x - 20 = 0

Δ = 500

√Δ = 10√5

x1 = 1 - √5

x2 = 1 + √5

 

Answer 2

a)

(x+3)²=(2x-1)²

 

x²+9=4x²+1  /- x² -1

 

8=3x²  /:3 

 

8/3=x²  /√

 

x=√8/3

 

b)

(3-4x)²=(5x-2)²

 

9+16x²=25x²+4 /-16x² -4

 

5=9x²  /:9

 

x²=5/9 /√

 

x=√5/9

 

c)

(2x-1)²=(3x+4)(x-3)+19

 

4x²+1=3x²-9x+4x-12+19

 

4x²+1=3x²-5x+7 /-3x² +5x -1

 

x²+5x=6   /√

 

√6x=6 /:6

x=1

 

d)

(x-4)²=(2x-3)(x+1)+1

 

x²+16=2x²+2x-3x-3+1

 

x²+16=2x²-x-2   /-x² +2

 

14=x²-x    /√

 

√

14=0

 

e)

(3x-2)(x+1)=(2x-3)(x+2)

 

3x²+3x-2x-2=2x²+4x-3x-6

 

3x²+x-2=2x²-x-6 / - 2x² +x +2

 

x²+2x=-4  / √

 

3x=-2 /:3

 

x=-2/3

 

f)

(3x-2)²-5(2x+3)=(2x-3)²

 

9x²+4-10x-15=4x²+9 

 

9x²-10x-11=4x²+9    / -4x² +11

 

5x²-10x=20 / √

 

5x=√20 /:5

 x= 2