Question

4x patrat +12x+9; 9x patrat -6x+1;4x patrat -20 +25;16x patrat-24+9

Answer 1

4x ² +12x+9= (2x)²+2*2x*3+3²=(2x+3)²
9x ² -6x+1=(3x)²-2*3x*1+1²=(3x-1)²
4x ²-20x +25=(2x)²-2*2x*5+5²=(2x-5)²

16x ²-24x+9=(4x)²-2*4x*3+3²=(4x-3)²


am aplicat formula a²+2ab+b²=(a+b)² si a²-2ab+b²=(a-b)²

Answer 2

$4 x^{2}$+12x+9

Δ=$b^{2}-4ac$

Δ=$12^{2}-4*4*9=144-144=0$
daca Δ=0⇒$x_{1}= x_{2}$
$x= \frac{-b+ \sqrt{delta} }{2a}$
$x= \frac{-12}{8}=- \frac{3}{2}$

b)$9x^{2}-6x+1$
Δ=$(-6)^{2}-4*1*9=36-36=0$

x=$\frac{-b}{2a}$

x=$\frac{6}{18}= \frac{1}{3}$

c)$4x^{2}-20x+25$

Δ=$20^{2} -4*4*25=400-400=0$

x=$\frac{20}{8}= \frac{5}{2}$

d)$16x^{2} -24x+9$

Δ=$24^{2} -4*9*16=576-576=0$

x=$\frac{24}{32}= \frac{3}{4}$