Question

rezolvati ecuatia: x la a 4 -17xla 2+16=0

Answer 1

x⁴-17x²+16=0   notam x²=t si vom avea:t²-17t+16=0
Δ=b²-4ac=(-17)²-4·1·16=289-64=225    √Δ=√225=15
t₁=(-b+√Δ)/2a=(17+15)/2=32/2=16
t₂=(-b-√Δ)/2a=(17-15)/2=2/2=1
t₁=16⇒x²=16⇒x₁=4;x₂=-4
t₂=1⇒x²=1⇒x₃=1;x₄=-1
solutiile ec.sunt{-4;4;-1;1}