Question

Determinati soluțiile ecuațiilor:
a)(x-2)la a doua-(x+1)la a doua=x-4
b)(2x+3)la a doua+7=4(x-2) la adoua
c)(3x+4)la a doua+20=5(x+1) la a doua+(2x-3)la a doua
Ma puteți ajuta,va rog!

Answer 1

$a) {(x - 2)}^{2} - {(x + 1)}^{2} = x - 4$

${x}^{2} - 4x + 4 - {x}^{2} - 2x - 1 = x - 4$

$- 4x - 2x - x = - 4 - 4 + 1$

$- 7x = - 7 \: | \div ( - 7)$

$x = 1$

$b) {(2x + 3)}^{2} + 7 = 4 {(x - 2)}^{2}$

$4 {x}^{2} + 12x + 9 + 7 = 4 {x}^{2} - 16x + 16$

$12x + 16x = 16 - 9 - 7$

$28x = 0$

$x = 0 \div 28$

$x = 0$

$c) {(3x + 4)}^{2} + 20 = 5 {(x + 1)}^{2} + {(2x - 3)}^{2}$

$9 {x}^{2} + 24x + 16 + 20 = 5 {x}^{2} + 10x + 5 + 4 {x}^{2} - 12x + 9$

$24x - 10x + 12x = 5 + 9 - 16 - 20$

$26x =- 22$

$x =- \frac{22}{26}$

$x = -\frac{11}{13}$