Question

Proszę o rozwiązanie:

a) (x+5) + (x+5)² = 0
b) (x-4)² - (x-4)² = 0
c)10(x-5)² = 25
d) (x-5) (x-8) (x-3)² = o
e) 8(x²+3x) = o

Dzięki ;)

Answer 1

A)

(x+5) + (x+5)² = 0
x+5+x²+10x +25 = 0
x²+11x+30-=0
Δ = 121 - 4*30 = 121 -120 = 1
√Δ = 1
x₁ = (-11+1)/2 = -5
x₂ = (-11-1)/2 = -6

b)

(x-4)² - (x-4)² = 0
x²-8x+16-x²+8x-16=0
0=0
x ∈ R

c)

10(x-5)² = 25
10(x²-10x+25) = 25
10x² -100x+250 = 25 |:5
2x² - 20x +50 = 5
2x²-20x+45 =0
Δ = 400 - 4*45*2 = 400 - 360 = 40
√Δ = √40 = 2√10
x₁ = (20+2√10)/4 = (10+√10)/2
x₂ = (20-2√10)/4 = (10-√10)/2

d)

(x-5) (x-8) (x-3)² = 0
1. x-5 = 0
x₁ = 5
2. x-8 = 0
x₂ = 8
3. (x-3)² = 0
x₃ = 3

e)

8(x²+3x) = o
8x(x+3) = 0
1. 8x = 0
x₁ = 0
2. x+3 = 0
x₂ = -3

Answer 2

A) (x+5) + (x+5)² = 0
(x+5)(1+x+5)=0
(x+5)(x+6)=0
x=-5 lub x=-6

b) (x-4)² - (x-4)² = 0
(x-4)²=(x-4)²
x∈R

c)10(x-5)² = 25
(x-5)² = 25/10 = (5/√10)² = 5√10/10 = √10/2
(x-5)² - (√10/2)²=0
(x-5 + √10/2)(x-5 - √10/2)=0
x=5-√10/2 lub x=5+√10/2

d) (x-5) (x-8) (x-3)² = 0
x=5 lub x=8 lub x=3

e) 8(x²+3x) = 0
x(x+3)=0
x=0 lub x=-3