Question

Rozwiaz rownanie:
a) x^2+x=4x+7
b)3x^2+1=7x
c)x^4-5x^2+6=0

d)x^4-9x^2=0

Answer 1

a) x^2+x=4x+7

x^2-3x-7=0

Δ=b²-4ac=9+28=37

√Δ=√37

x₁=(-b-√Δ)/2a=(3-√37)/2

x₂=(-b+√Δ)/2a=(3+√37)/2

 

b)3x²+1=7x

3x²-7x+1=0

Δ=49-12=37

√Δ=√37

x₁=(7-√37)/6

x₂=(7+√37)/6

 

c)x⁴-5x²+6=0                      x²=k

k²-5k+6=0

Δ=25-24=1

√Δ=1

k₁=(5-1)/2=2

k₂=(5+1)/2=3

k=x²

x₁=√k₁=√2  ∨   x₁=-√2

x₂=√k₂=√3  ∨    x₂=-√3

 

d)x⁴-9x²=0 

x²(x²-9)=0

x²(x-3)(x+3)=0

x₁=0 ∨ x₂=3 ∨ x³=-3