Question

Cum descompun in factori
a) 7-2√7x+x²
b) (2√5)²-4√5z+z²
c) 20z²+4z√5+1

Answer 1

Formula (a-b)^2=a^2-2ab+b^2
a)$a)x^{2} -2 \sqrt{7} x+7=(x- \sqrt{7} )(x- \sqrt{7} )$
b)$b)z^{2} -4 \sqrt{5}*z+ (2 \sqrt{5} )^{2} =(z-2 \sqrt{5} )(z-2 \sqrt{5} )$
c)$20 z^{2} +4z \sqrt{5} +1= (\sqrt{20} z+1)(\sqrt{20} z+1)$

Answer 2

a)x²-2√7x+7=
Δ=(2√7)²-4·7=4·7-28=28-28=0
x1=x2=2√7/2=√7
x²-2√7x+7==(x-√7)(x-√7)=(x-√7)²

b) (2√5)²-4√5z+z²=
z²-4√5z+20=
Δ=(4√5)²-4·20=80-80=0
z1=z2=4√5/2=2√5
(2√5)²-4√5z+z²=(z-2√5)(z-2√5)=(z-2√5)²

c) 20z²+4z√5+1
Δ=(4√5)²-4·20=80-80=0
z1=z2=-4√5/20=-√5/5
 20z²+4z√5+1=(z+√5/5)²