Question

a) (x+5) la puterea a 2 a +(x-6)(x+6)=2(x+3)+15

b) 2(x-5)-7=3(7+3)

Va rog... multumesc

Answer 1

$a) \\ \\ {2x}^{2} + 10x - 11 = 2x + 21 \\ \\ {2x}^{2} + 10x - 11 - 2x - 21 = 0 \\ \\ {2x}^{2} + 8x - 32 = 0 \\ \\ \frac{ - 8 + \sqrt{320} }{4} = x \\ \\ \frac{ - 8 - \sqrt{320} }{4} = x \\ \\ b) \\ \\ 2x - 17 = 3 \times (10) \\ \\ 2x - 17 = 30 \\ \\ 2x = 30 + 17 \\ \\ 2x = 47 \\ \\ x = 23 \frac{1}{2}$

Answer 2

a)

( x + 5)²+ ( x - 6 ) ( x + 6 ) = 2 ( x + 3) + 15

x²+ 10 x + 25 + x² - 36 = 2 x + 6 + 15

2 x² + ( 10 x - 2 x) - 11 - 21 = 0

2 x² + 8 x - 32 = 0

Δ= 64 + 4 × 2 × 32 = 64 + 256 = 320

x₁ = ( - 8 + √ 320 ) / 4 = ( - 8 + 8 √5) / 4 = 8 ( √5 - 1) / 4 = 2( √5 - 1 )

x₂ = ( - 8 - 8√5 ) / 4 = - 2 ( √5 + 1)

b)

2(x-5)-7=3(7+3)

2 x - 10 - 7 = 30

2 x = 30 + 17

2 x = 47

x = 47 / 2 = 23 intregi si 1 / 2

→ iar daca in paranteza e un ,,x ", atunci solutia este:

b)

2 ( x - 5 ) - 7 = 3 ( 7 x + 3 )

2 x - 10 - 7 = 21 x + 9

2 x - 21 x = 9 + 17

- 19 x = 26

x = - 26 / 19

sau daca in loc de 7 este ,, x "

2 ( x - 5 ) - 7 = 3 ( x + 3 )

2 x - 10 - 7 = 3 x + 9

2 x - 3 x = 9 + 17

- x = 26

x = - 26