Question

Rozwiaz
{ 3x - 2y = 8
{ 2x + y = 3
to jest jedno zadanie polaczone tym nawiasem

b) x² + 4x - 12 = 0
c) 2x² + 10x - 12 ≤ 0
te 3 zadanka prosze rozwiazac oczywiscie daje naj tylko prosze o czytelne rozwiazania

Answer 1

{3x -2y = 8
{2x+y = 3 /*2

{3x-2y=8
{4x+2y=6
+________
7x=14 /:7
x=2

6-2y=8
-2y=2
y=-1

{x=2
{y=-1

b) a=1 b= 4 c=-12
Δ= b²-4ac
Δ=16 +48
Δ=64
√Δ= 8

x₁= -4-8/ 2 = -12/2 = -6
x₂= -4+8/2 = 4/2 = 2

c) a = 2 b = 10 c=-12
Δ= 100=96
√Δ= 2

x₁= -10-2/4 = -12/4 = -3
x₂ = -10+2/4 = -8/4 = -2

Answer 2

{ 3x - 2y = 8
{ 2x + y = 3/*2
[3x-2y=8
[4x+2y=6
`````````
__7x=14/:7
___x=2
3x-2y=8
3*2-2y=8
6-2y=8
-2y=8-6
-2y=2/:(-2)
__y=-1
{x=2
{y=-1
b) x² + 4x - 12 = 0_____dla a=1 b=4 c=-12
Δ=b²-4ac=4²-4*1*(-12)=16+48=64
x₁=-b+√Δ/2a=⁻⁴⁺⁸/₂*₁=⁴/₂=2
x₂=-b-√Δ/2a=⁻⁴⁻⁸/₂*₁=⁻¹²/₂=-6
x² + 4x - 12=0
1(x-2)(x-(-6)=0
(x-2)(x+6)=0
c) 2x² + 10x - 12 ≤ 0
Δ=b²-4ac=10²-4*2*(-12)=100+96=196
x₁=-b-√Δ/2a=⁻¹⁰⁺¹⁴/₂*₂=⁴/₄=1
x₂=-b+√Δ/2a=⁻¹⁰⁻¹⁴/₂*₂=⁻²⁴/₄=-6
2x² + 10x - 12 ≤ 0
2(x-1)(x-(-6))≤0
2(x-1)(x+6)≤0