Question

Rozwiąż (daje naj)
a) 3( 2x -1) + 5x = 2- [ 4x - (1 - 2x)]
b) x ( x +1) - ( x² + 1) < 2 ( -x + 3 )
c){ 3x - 2y = 8
{ 2x + y = 3 to jest jedno zadanie polaczone tym nawiasem z boku

d) x² + 4x - 12 = 0
e) 2x² + 10x - 12 ≤ 0

Answer 1

A) 3( 2x -1) + 5x = 2- [ 4x - (1 - 2x)]
6x-3+5x=2-4x+1-2x
17x=6
x=17/6

b) x ( x +1) - ( x² + 1) < 2 ( -x + 3 )
x²+x-x²-1<-2x+6
3x<7
x<7/3

c){ 3x - 2y = 8
2x + y = 3 /*2
3x-2y=8
4x+2y=6
----------------------
7x=14
x=2

d) x² + 4x - 12 = 0
x²+4x=12
e) 2x² + 10x - 12 ≤ 0
2x²+10x≤12

f) x+3 4x 2x -1
←→ + →← = ←→→ + 2 /*6
2 3 6
3x+9+8x=2x-1+2
9x=-8
x=8/9

Answer 2

A) 3( 2x -1) + 5x = 2- [ 4x - (1 - 2x)]
6x - 3 + 5x = 2 - (4x - 1 + 2x)
11x - 3 = 2 - 4x + 1 - 2x
11x + 4x + 2x = 2 + 1 + 3
17x = 6
x = 6/17
b) x ( x +1) - ( x² + 1) < 2 ( -x + 3 )
x² + x - x² - 1< - 2x + 6
x + 2x < 6 + 1
3x < 7
x < 7/3
c){ 3x - 2y = 8
{ 2x + y = 3 mnożymy przez 2
3x - 2y = 8
4x + 2y = 6
dodajemy stronami
3x + 4x - 2y + 2y = 8 + 6
7x = 14
x = 14/7 = 2
d) x² + 4x - 12 = 0
Δ = 16 + 48
Δ = 64
√Δ = √64 = 8
x1 = - 4 - 8/2 = - 12/2 = - 6
x2 = - 4 + 8/2 = 4/2 = 2
e) 2x² + 10x - 12 ≤ 0
Δ = 100 + 96 = 196
√Δ = √196 = 14
x1 = - 10 - 14/2 = - 24/2 = - 12
x2 = - 10 + 14/2 = + 4/2 = 2

(x - x1)(x - x2)≤0
x - x1 ≤ 0 i x - x2 ≥ 0 lub x - x1≥ 0 i x - x2 ≤ 0
x ≤ 12 i x ≥ - 2 lub x ≥ 12 i x ≤ - 2
odp
x ≤ 12 i x ≥ - 2 jest to przedział ( - 2 , 12)