Question

5.Rezolvați ecuațiile următoare utilizând metoda descompuneri în facturi. va rog dau 69 de puncte

Answer 1

a)

$x^{2} - 10x + 9 = x^{2} -9x -x + 9 = x(x-9)-(x-9) = (x-9)(x-1)$

$(x-9)(x-1) = 0 \implies x = 1;x=9$

b)

$x^{2} + 8x + 15 = x^{2} + 3x + 5x + 15 = x(x+3)+5(x+3) = (x+3)(x+5)$

$(x+3)(x+5) = 0 \implies x = 3;x=5$

c)

$3x^{2} +11x+8=3x^{2} + 8x + 3x + 8 =x(3x+8) + (3x+8) = (3x+8)(x+1)$

$(3x+8)(x+1) = 0 \implies x=-\dfrac{8}{3};x=-1$

d)

$6x^{2} - 17x + 10 = 6x^{2} -5x -12x + 10 = x(6x-5)-2(6x-5) = (6x-5)(x-2)$

$(6x-5)(x-2) = 0 \implies x = \dfrac{5}{6};x=2$

e)

$3x^{2} +8x+4 =3x^{2} +2x+6x+4=x(3x+2)+2(3x+2)=(3x+2)(x+2)$

$(3x+2)(x+2) = 0 \implies x=-2;x=-\dfrac{2}{3}$

f)

$x^{2} +8x-20=x^{2} +10x-2x-20=x(x+10)-2(x+10)=(x+10)(x-2)$

$(x+10)(x-2)=0 \implies x=-10;x=2$

g)

$x^{2} -3x-40=x^{2} +5x-8x-40=x(x+5)-8(x+5)=(x+5)(x-8)$

$(x+5)(x-8)=0 \implies x=-5;x=8$

h)

$5x^{2} +8x-21=5x^{2} -7x+15x-21=x(5x-7)+3(5x-7)=(5x-7)(x+3)$

$(5x-7)(x+3)=0 \implies x=-3;x=\dfrac{7}{5}$