Question

Rezolvati :

a. (x+2)(x+3)
b. (x-2)(x-3)
c. (6x-1)(3x-3)
d. (x²+2)(x-5)
e.(6x²-1)(2x-2)
f. (x-3)(x²+3x+9)

Mi am dat toate punctele. Repede pls

Answer 1

$a)(x + 2)(x + 3)$

$= {x}^{2} + 3x + 2x + 6$

$= {x}^{2} + 5x + 6$

${x}^{2} + 5x + 6=0$

$a=1;b=5;c=6$

$/Delta={b}^{2}-4\times a\times c$

$\Delta={5}^{2}-4\times1\times6$

$\Delta=25-24$

$\Delta=1$

$x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2\times a}$

$x_{1,2}=\frac{-5\pm\sqrt{1}}{2\times 1}$

$x_{1,2}=\frac{-5\pm1}{2}$

$x_{1}=\frac{-5+1}{2}=-\frac{4}{2}=-2$

$x_{2}=\frac{-5-1}{2}=-\frac{6}{2}=-3$

$b)(x - 2)(x - 3)$

$= {x}^{2} - 3x - 2x + 6$

$= {x}^{2} - 5x + 6$

$c)(6x - 1)(3x - 3)$

$= {18x}^{2} - 18x - 3x + 3$

$= {18x}^{2} - 21x + 3$

$a=18;b=-21;c=3$

$\Delta={b}^{2}-4\times a\times c$

$\Delta={(-21)}^{2}-4\times18\times3$

$\Delta=441-216$

$\Delta=225$

$x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2\times a}$

$x_{1,2}=\frac{-(-21)\pm\sqrt{225}}{2\times 18}$

$x_{1,2}=\frac{21\pm15}{36}$

$x_{1}=\frac{21+15}{36}$

$x_{1}=\frac{36}{36}$

$x_{1}=1$

$x_{2}=\frac{21-15}{36}$

$x_{2}=\frac{6}{36}$

$x_{2}=\frac{1}{6}$

$d)( {x}^{2} + 2)(x - 5)$

$= {x}^{3} - 5 {x}^{2} + 2x- 10$

$D_{10}=\pm1,\pm2,\pm5,\pm10$

$=>x=5$

${x}^{2}+2=0$

${x}^{2}=-2$

$x=/pm\:sqrt{-2}$

$=>ecuatia\: nu\: are\: radacini \:reale$


$e)(6 {x}^{2} - 1)(2x - 2)$

$= 12 {x}^{3} - 12 {x}^{2} - 2x + 2$

$12{x}^{3}-12{x}^{2}-2x+2=0$

$D_{2}=\pm1,\pm2$

$=>x_{1}=1$

$12{x}^{2}-2=0$

$12{x}^{2}=2$

${x}^{2}=\frac{2}{12}$

${x}^{2}=\frac{1}{6}$

$x=\sqrt{\frac{1}{6}}$

$x=\pm\frac{\sqrt{6}}{6}$

$x_{1}=\frac{\sqrt{6}}{6}$

$x_{2}=-\frac{\sqrt{6}}{6}$

$f)(x - 3)( {x}^{2} + 3x + 9)$

$= {x}^{3} + 3 {x}^{2} + 9x - 3 {x}^{2} - 9x - 27$

$= {x}^{3} - 27$

${x}^{3}-27=0$

${x}^{3}=27$

${x}^{3}={3}^{3}$

$=>x=3$

Answer 2

a. x^2 + 5x+6
b. x^2 -5x  + 6
c. 18x^2 -21x +3
d. x^3 -5x^2 +2x -10
e. 12x^3 -12x^2 -2x + 2
f. x^3 +3x^2 +9x -3x^2 -9x -27 = x^3 -27