Question

1) x la puterea a 2a - 10x + 16=0 2) x la puterea a 2a - 4x +4 =0 3) 5x la puterea a 2a +4x+1=0​

Answer 1

Răspuns:

$a) \: {x}^{2} - 10x + 16 = 0 \\ a = 1 \\ b = - 10 \\ c = 16 \\ delta = {b}^{2} - 4ac \\ delta = { (- 10)}^{2} - 4 \times 1 \times 16 \\ delta = 100 - 64 = 36 \\ \sqrt{delta} = \sqrt{36} ={6 } \\ x1.2= \frac{ - b - + \sqrt{delta} }{2a} \\ x1 = \frac{ - ( - 10) - 6}{2} = \frac{10 - 6}{2} = \frac{4}{2} = 2 \\ x2 = \frac{ - ( - 10) + 6}{2} = \frac{10 + 6}{2} = \frac{16}{2} = 8$

$b) \: \: {x}^{2} - 4x + 4= 0 \\ a = 1 \\ b = - 4 \\ c = 4 \\ delta = {b}^{2} - 4ac \\ delta = { (- 4)}^{2} - 4 \times 1 \times 4 \\ delta = 16 - 16 =0 \\ \sqrt{delta} = \sqrt{0} ={0} \\ x1.2= \frac{ - b - + \sqrt{delta} }{2a} \\ x1 .2= \frac{ - ( - 4) - 0}{2} = \frac{4}{2} = 2$

$c) \: {5x}^{2} + 4x +1 = 0 \\ a = 5 \\ b = 4 \\ c = 1 \\ delta = {b}^{2} - 4ac \\ delta = { 4}^{2} - 4 \times 5 \times 1\\ delta = 16- 20 = - 4 \\ delta < 0 \\ ecuatia \: nu \: are \: solutie$