Question

Rezolvati ecuatiile :
a)x la patrat +6x=16
b)x la patrat +2x=8
c)4x la patrat -4x=8
d)x la patrat -8x=-7

Answer 1

Il rezolv pe a) ca model si pe urma iti va fi usor sa le faci si pe restul.

a) x^2 +6x = 16

Trecem ce e dupa egal in stanga si vom avea:
x^2 +6x - 16 = 0

Delta = b^2 - 4ac = 6*6 -(4 *1 *-16) = 36+64 =100

X1 = (-b +  radical din delta ) /2a = (-6 + 10) / 2 = 4/2 = 2

X2 = (-b -  radical din delta ) /2a = (-6 - 10)/2 = -16 /2 = -8

Answer 2

    
$a)\\ x^{2} +6x=16\\x^{2} +6x-16=0 \\ x_{12}= \frac{-6 \pm \sqrt{ 6^{2}+4*16}}{2}= \frac{-6 \pm \sqrt{ 36+64}}{2}=\frac{-6 \pm \sqrt{100}}{2}= \frac{-6 \pm 10}{2}= -3 \pm 10 \\ x_1 = -3 + 10 = \boxed{7} \\ x_2 = -3 - 10 = \boxed{-13}$


$b)\\ x^{2} +2x=8\\ x^{2} +2x-8=0 \\ x_{12}= \frac{-2 \pm \sqrt{ 2^{2}+4*8}}{2}= \frac{-2 \pm \sqrt{ 4+32}}{2}=\frac{-2 \pm \sqrt{36}}{2}= \frac{-2 \pm 6}{2}= -1 \pm 3 \\ x_1 = -1 + 3 = \boxed{2} \\ x_2 = -1 - 3 = \boxed{-4}$


$c)\\ 4x^{2} -4x=8 \\ 4x^{2} -4x -8=0 \\ x_{12}= \frac{4 \pm \sqrt{ (-4)^{2}+4*4*8}}{2}= \frac{4 \pm \sqrt{ 16+128}}{2}=\frac{4 \pm \sqrt{144}}{2}= \frac{4 \pm 12}{2}= 2 \pm 6 \\ x_1 = 2 + 6 = \boxed{8} \\ x_2 = 2 - 6 = \boxed{-4}$


$d)\\ x^{2} -8x=-7 \\ x^{2} -8x+7=0 \\ x_{12}= \frac{8 \pm \sqrt{ (-8)^{2}-4*7}}{2}= \frac{8 \pm \sqrt{ 64-28}}{2}=\frac{8 \pm \sqrt{36}}{2}= \frac{8 \pm 6}{2}= 4\pm 3 \\ x_1 = 4 + 3 = \boxed{7} \\ x_2 = 4 - 3 = \boxed{1}$