Răspuns :
[tex]a)(x-5)^2=x^2-2x5+5^2\\
x^2-10x+25\\\\
b)(x+5)(x-5)=x^2-5^2\\
x^2-25\\\\
c)x^2-6x+9=(x-3)^2\\\\
d)x^2-9=(x+3)(x-3)
[/tex]
Ο1 ) (x-5)²=(x-5)(x-5)=x²-5x-5x+10==>x²-10x+10=0
Ф2) (x+2)²=(x+2)(x+2)=x²+2x+2x+4=x²+4x+4=0
Θ3 ) (x+5)(x-5)=x²-5x+5x-10==>x²-10=0 =>x=0
Ω4) x²-6x+9=0 || a=1 || b=-6 || c=9
Δ=b²-4ac x₁,₂=[-b(+-)√Δ]/2a
Δ=(-6)²-4*1*9 x₁=x₂=6(+-)0/2=6/2=3
Δ=36-36
Δ=0
Ψ5) x²-9=0 ||a=1 || b=0 || c=-9
Δ=b²-4ac x₁=0-6/2=-6/2=-3
Δ=(0)²-4*1*(-9) x₂=0+6/2=6/2=3
Δ=36=>√Δ=√36=6 x∈(-3;3)
Ф2) (x+2)²=(x+2)(x+2)=x²+2x+2x+4=x²+4x+4=0
Θ3 ) (x+5)(x-5)=x²-5x+5x-10==>x²-10=0 =>x=0
Ω4) x²-6x+9=0 || a=1 || b=-6 || c=9
Δ=b²-4ac x₁,₂=[-b(+-)√Δ]/2a
Δ=(-6)²-4*1*9 x₁=x₂=6(+-)0/2=6/2=3
Δ=36-36
Δ=0
Ψ5) x²-9=0 ||a=1 || b=0 || c=-9
Δ=b²-4ac x₁=0-6/2=-6/2=-3
Δ=(0)²-4*1*(-9) x₂=0+6/2=6/2=3
Δ=36=>√Δ=√36=6 x∈(-3;3)
