Question

Rozwiąż równanie kwadratowe:
3x(x+2)+(2x-1)²=1-5x

(x+1)(x-1)+2x(2x+1)=6x²

(3x-2)²-x²-2x=1

(1-3x)²+3x-4x²=9

(2x-3)²=8x

(4-3x)²=16-3x²

(x+4)²=5(x+14)

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

2x²+9=(x+4)²+14x

(x+4)²=9-8x

(x+3)²=3(2x+6)

(2x-3)²-(3x-2)²=5

(x-2)²=x+4+2(x-5)(x+5)

Bardzo proszę pomóżcie mi jest to potrzebne do poprawki z matmy
Proszę o rozpisane danych przykładów
Dziękuję

Answer 1

3x(x +2) + (2x - 1)² = 1 - 5x
3x² + 6x + 4x² - 4x +1 = 1 - 5x
7x² + 7x = 0
7x(x + 1) = 0
x = 0 lub x + 1 = 0
x1 = 0
x2 = -1
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(x+1)(x-1) +2x(2x +1) = 6x²
x² -1 + 4x² + 2x = 6x²
x² - 2x + 1 = 0
(x -1)² = 0
x -1 = 0
x = 1 - podwójny
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(3x -2)² - x² - 2x = 1
9x² -12x +4 - x² -2x -1 = 0
8x² -14x + 3 = 0
Δ = (-14)² - 4*8*3 = 196 -96 = 100
√Δ = 10
x1 = [14 - 10]/16 = 4/16 = 1/4
x2 = [14 + 10] /16 = 24/16 = 3/2
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(1 -3x)² + 3x - 4x² = 9
1 - 6x + 9x² +3x - 4x² - 9 = 0
5x² -3x - 8 = 0
Δ = 9 - 4*5*(-8) = 9 + 160 = 169
√Δ = 13
x1 = [3 - 13]/10 = -10/10 = - 1
x2 = [3 + 13]/10 = 16/10 = 1,6
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(2x - 3)² = 8x
4x² -12x +9 - 8x = 0
4x² - 20x + 9 = 0
Δ = 400 - 4*4*9 = 400 - 144 = 256
√Δ = 16
x1 = [20 - 16]/8 = 4/8 = 1/2
x2 = [20 + 16]/8 = 36/8 = 4,5
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(4 - 3x)² = 16 - 3x²
16 - 24x +9x² -16 + 3x² = 0
12x² - 24x = 0
12x(x - 2) = 0
x = 0 lub x - 2 = 0
x1 = 0 oraz x2 = 2
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(x +4)² = 5( x + 14)
x² + 8x +16 = 5x + 70
x² +3x - 54 = 0
Δ = 9 -4*1*(-54) = 9 + 216 = 225
√Δ = 15
x1 = [-3 -15]/2 = -9
x2 = [-3 + 15]/2 = 6
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(x +1)(x -1) = (x -1)(3 - x)
x² - 1 = 3x -x² - 3 + x
x² -1 = -x² + 4x - 3
2x² - 4x +2 = 0 / : 2
x² - 2x + 1 = 0
(x - 1)² = 0
x - 1 = 0
x = 1 ( podwójny)
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2x² + 9 = ( x +4)² + 14 x
2x² + 9 = x² +8x + 16 + 14 x
x² -22x - 7 = 0
Δ = 484 -4*1*(-7) = 484 +28 = 512
√Δ = 16√2
x1 = [22 - 16√2]/2 = 11 -8√2
x2 = [22 + 16√2]/2 = 11 + 8√2
-------------------------------------------------------------
( x + 4)² = 9 - 8x
x² +8x + 16 - 9 + 8x = 0
x² +16x + 7 = 0
a = 1 , b = 16, c = 7
Δ = b² - 4ac =16² -4*1*7 = 256 - 28 = 228 = 4*57
√Δ = 2√57
x1 = [-b - √Δ]/(2a) = [ -16 - 2√57]/2 = -8 - √57
x2 = [-b + √Δ ]/(2a) = [ -16 +2√57]/2 = -8 + √57
------------------------------------------------------------
(x +3)² = 3(2x + 6)
x² +6x + 9 = 6x + 18
x² = 9
x1 = - 3
x2 = 3
--------------------------------------------------------
(2x - 3)² - (3x - 2)² = 5
4x² - 12x + 9 - 9x² +12x -4 - 5 = 0
-5x² = 0
x = 0
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(x -2)² = x + 4 +2(x-5)(x+5)
x² -4x + 4 = x + 4 +2(x² - 25)
x² -4x + 4 = x + 4 + 2x² - 50
-x² - 5x + 50 = 0
Δ = 25 -4*(-1)*50 = 25 + 200 = 225
√Δ = 15
x1 = [5 -15]/(-2) = -10/(-2) = 5
x2 = [5+15]/(-2) = 20 /(-2) = -10
==================================================

Answer 2

A)3x(x+2)+(2x-1)²=1-5x
3x²+6x+4x²-4x+1=1-5x
7x²+2x+1=1-5x
7x²+7x=0
7x(x+1)=0
7x=0
x=0

x+1=0
x=-1

b)(x+1)(x-1)+2x(2x+1)=6x²
x²-1+4x²+2x=6x²
5x²+2x-1=6x²
-x²+2x-1=0
Δ=2²-4*(-1)*(-1)=4-4=0

x=-2/-2=1

c)(3x-2)²-x²-2x=1
9x²-12x+4-x²-2x=1
8x²-14x+4=1
8x²-14x+3=0
Δ=(-14)²-4*8*3=196-96=100
√Δ=10
x₁=14+10/16=24/16=1½
x₂=14-10/16=4/16=¼


d)(1-3x)²+3x-4x²=9
1 -6x+9x²+3x- 4x²- 9 = 0
5x² -3x - 8 = 0
Δ = 9 - 4*5*(-8) = 9 + 160 = 169
√Δ = 13
x1 = 3 - 13/10 = -10/10 = - 1
x2 = 3 + 13/10 = 16/10 = 1⅔

e)(2x-3)²=8x
4x²-12x+9=8x
4x²-20x+9=0
Δ=(-20)²-4*4*9=400-144=256
√Δ=16
x₁=20+16/8=36/8=4½
x₂=20-16/8=4/8=½


f)(4-3x)²=16-3x²
16-24x+9x²=16-3x²
12x²-24x=0
12x(x-2)=0
12x=0
x=0

x-2=0
x=2

g)(x+4)²=5(x+14)
x²+8x+16=5x+70
x²+3x-54=0
Δ=3²-4*1*(-54)=9+216=225
√Δ=15
x₁=-3+15/2=12/2=6
x₂=-3-15/2=-18/2=-9

h)(x+1)(x-1)=(x-1)(3-x)
x² - 1 = 3x -x² - 3 + x
x² -1 = -x² + 4x - 3
2x² - 4x +2 = 0
x² - 2x + 1 = 0
Δ=(-2)-4*1*1=4-4=0
x=2/2=1


i)2x²+9=(x+4)²+14x
2x²+9=x²+8x+16+14x
2x²+9=x²+22x+16
x²-22x-7=0
Δ=(-22)²-4*1*7=484+28=512
√Δ=√512
x₁=22+√512/2
x₂=22-√512/2

j)(x+4)²=9-8x
x²+8x+16=9-8x
x²+16x+7=0
Δ=16²-4*1*7=256-28=228
√Δ=√228
x₁=-16+√228/2
x₂=-16-
√228/2

k)(x+3)²=3(2x+6)
x²+6x+9=6x+18
x²-9=0
x²=9
x=3 lub x=-3

l)(2x-3)²-(3x-2)²=5
4x² - 12x + 9 - 9x² +12x -4=5
-5x² = 0
x =0

m)(x -2)² = x + 4 +2(x-5)(x+5)
x² -4x + 4 = x + 4 +2(x² - 25)
x² -4x + 4 = x + 4 + 2x² - 50
-x² - 5x + 50 = 0
Δ = 25 -4*(-1)*50 = 25 + 200 = 225
√Δ = 15
x1 = 5 -15/-2 = -10/-2 = 5
x2 = 5+15/-2= 20 /-2 = -10