Question

Rozwiąż równanie :

a. -x⁴ + 7x² = 3 ( x⁴ +1 )
b. (5x - 8 )(4 - 3x) + x(4-x)=0
c. (2x-3)(x+5) = (5x+9)(6+3x)
d. x(2x+7)-5 = (x+4)(5-x)
e. (3x - 1)(2-x)-x(x+3)=2

bardzo proszę o pomoc . :)

Answer 1

A. -x⁴ + 7x² = 3 ( x⁴ +1 )
-x⁴ + 7x² - 3(x⁴ +1) = 0
-x⁴ + 7x² - 3x⁴ - 3 = 0
-4x⁴ + 7x² - 3 = 0
4x⁴ - 7x² + 3 = 0
x² = t i t>=0
4t² - 7t + 3 = 0
Δ=1; √Δ = 1
t₁ = 7-1/8 = 3/5
t₂ = 7+8/8 = 1 --> x₁ = 1 v x₂ = -1 v x₃ = 3√5/5 v x₄ = -3√5/5

b. (5x - 8 )(4 - 3x) + x(4-x)=0
20x - 15x² - 32 - 24x +4x - x² = 0
-16x² + 48x - 32 = 0 /:-16
x² - 3x + 2 = 0
Δ=1; √Δ = 1
x₁ = 3-1/2 = 1
x₂ = 3+1/2 = 2

c. (2x-3)(x+5) = (5x+9)(6+3x)
2x² + 10x - 3x - 15 - 30x - 15x² - 54 - 27x = 0
-13x² - 50x - 69 = 0
13x² + 50x + 69 = 0
Δ<0 --> brak rozwiązania

d. x(2x+7)-5 = (x+4)(5-x)
2x² + 7x - 5 - 5x + x² -20 + 4x = 0
3x² + 6x - 25 = 0
Δ=336; √Δ = 4√21
x₁ = -6-4√21/6
x₂ = -6+4√21/6

e. (3x - 1)(2-x)-x(x+3)=2
6x - 3x² - 2 + x - x² - 3x - 2 = 0
-4x²+ 4x - 4 = 0 /:-4
x² - x + 1 = 0
Δ<0 --> brak rozwiązania