Question

3)Rozwiąż równanie a) x2( x kwadrat) - 8x+14=o b) x6( x do szóstej) -9x3(minus x do trzeciej)+8=0

Answer 1

a)

x²-8x+14=0

Δ=64-56=8

√Δ=2√2

 

x1=8-2√2/2 = 2(4-√2)/2=4-√2

x2=8+2√2/2=4+√2

 

b)

x⁶-9x³+8=0

x³=t

 

   t²-9t+8=0

Δ=81-32=49

√Δ=7

t1=9-7/2 = 2/2=1

t2=9+7/2=16/2=8

 

     x³=t      

  x₁³=t1      U       x₂³=t2

x₁³=1                   x₂³=8

   x₁=1                  x₂=2

 

Answer 2

a)

Δ=64-56=8

√Δ=√8=2√2

x=4-√2 v x=4+√2

albo sprytniej

(x-4)²-2=0

(x-4-√2)(x-4+√2)=0

b)

x³=t

t²-9t+8=0

t²-t-8t+8=0

t(t-1)-8(t-1)=0

(t-1)(t-8)=0

t=1 v t=8

x3=1 v x³=8

x=1 v x=2