a)
(2-3\sqrt3)^2 =2^2-2*2*3\sqrt3+(3\sqrt3)^2=4-12\sqrt3+9*3=31-12\sqrt3
b)
(4x+\sqrt3)^2 =16x^2+8\sqrt3x+3
c)
(x-\sqrt3) (x+\sqrt3) =x^2-(\sqrt3)^2=x^2-3
d)
(2\sqrt5 - 3\sqrt2)^2 =4*5-12\sqrt{10}+9*2=38-12\sqrt{10}
Zadanie 2
Doprowadź do najprostszej postaci:
3(x-1)^2 - 4(x-3) (x+3) =3(x^2-2x+1)-4(x^2-9)=3x^2-6x+3-4x^2+36=-x^2-6x+39
Zadanie 3
Rozwiąż:
2( x-1 )^2-4(x+2)^2 \leq -2x^2
2(x^2-2x+1)-4(x^2+4x+4)\leq-2x^2
2x^2-4x+2-4x^2-16x-16\leq-2x^2
-2x^2-20x-14\leq-2x^2 |-2x^2
-20x\leq14 |:(-20)
x\geq-\frac{14}{20}
x\geq -\frac{7}{10}
x\in \langle -\frac{7}{10};+\infty)