Question

ex, 5 daca puteti sa ma ajutati multumesc mult!

Answer 1

Explicație pas cu pas:

a)

${(x + 1)}^{2} - {(x - 1)}^{2} = 4 \\ (x + 1 + x - 1)(x + 1 - x + 1) = 4 \\ 2x \cdot 2 = 4 < = > 4x = 4 = > x = 1$

b)

$(2x - 1)^{2} = 8 + (3 - 2x)^{2} \\ (2x - 1)^{2} - (3 - 2x)^{2} = 8 \\ (2x - 1 + 3 - 2x)(2x - 1 - 3 + 2x) = 8 \\ 2 \cdot4 (x - 1) = 8 < = > x - 1 = 1 \\ = > x = 2$

c)

$2x - 3 \not = 0 = > x\not = \frac{3}{2} \\ 2x + 4 \not = 0 = > x\not = - 2$

$\frac{5x + 4}{2x - 3} = \frac{5x - 7}{2x + 4} \\ (5x + 4)(2x + 4) = (5x - 7)(2x - 3)$

$10 {x}^{2} + 20x + 8x + 16 = 10x^{2} - 15x - 14x + 21 \\ 28x + 29x = 21 - 16 < = > 57x = 5 \\ = > x = \frac{5}{57}$

d)

$(x + 1)(x - 2) + (x - 1)(x + 2) = 2({x}^{2} - 4) \\ {x}^{2} - 2x + x - 2 + {x}^{2} + 2x - x - 2 = 2 {x}^{2} - 8 \\ {2x}^{2} - 4 = 2 {x}^{2} - 8 < = > - 4 = - 8 \\fals = > x = Ø$