Question

Rezolvati urmatoarele ecuatii: ( unde t este necunoscuta )
a) t^2 + ( x- 1) t = 6 - 2x
b) 4^x + (x -1) * 2^x + 2x = 6

Answer 1

a)Δ=b²-4ac
Δ=(x-1)²-4(-6+2x)=x²-2x+1+24-8x=x²-10x+25=(x-5)²
√Δ=x-5
x₁=(-x+1-x+5)/2=(-2x+6)/2=2(-x+3)/2=-x+3
x₂=(-x+1+x-5)/2=-6/2=-3

b)notam 2ˣ=t
t²+(x-1)t+2x-6=0
Δ=b²-4ac
Δ=(x-1)²-4(2x-6)=x²-10x+25=(x-5)²
√Δ=x-5
x₁=-x+3
x₂=-3