Question

Valendo 65 Pontos Resolva As Equações : A) 9x²-35 = 4x -15
B) 5.(x-3) -2 (x+2) = 3 -5 x

Answer 1

A) 9x² -35 = 4x -15 
9x² - 4x -35 + 15 = 0
9x² -4x - 20 = 0

a = 9
b = -4
c = -20

Δ = b² -4 .a . c 
Δ= (-4)² -4 . 9 . (-20)
Δ = 16 -36 . (-20)
Δ = 16 + 720
Δ = 736

$\mathtt{\dfrac{-b+-\sqrt{\Delta}}{2~~.~a}~~=~~ \dfrac{-(-4)+-\sqrt{736}}{2~~.9}~~=~~ \dfrac{4 +-\sqrt{736}}{18}}$

736    |4
184    |4
46      |2
23      |23
1 

4² . 2 . 23
4² . 46

$\mathtt{ \dfrac{4 +-\sqrt{736}}{18}~~=~~ \dfrac{4+- \sqrt{46~.~4^2}}{18}~~~=~~ \dfrac{4+-~ 4\sqrt{46}}{18} ~~(\div2) } \\ \\ \\ \mathtt{\dfrac{2+-~2\sqrt{46}}{9}} \\ \\ \\ \mathtt{x' =\dfrac{2+~2\sqrt{46}}{9}~~= ~~ \boxed{\dfrac{2\sqrt{246}+ 2}{9}}}\\ \\ \\ \matht{x'' = \dfrac{2 - ~2\sqrt{46}}{9}~~=~~ \boxed{-\dfrac{2\sqrt{46}-2}{9}}}$

b)
5(x - 3) - 2(x+2) = 3 - 5x
5x - 15 - 2x - 4 = 3 - 5x
5x - 2x - 15 - 4 =- 5x + 3
3x - 19 = -5x + 3
3x + 5x = 3 + 19
8x = 22
x = 22/8

Answer 2

Resposta:

A) 9x² -35 = 4x -15  

9x² - 4x -35 + 15 = 0

9x² -4x - 20 = 0

a = 9

b = -4

c = -20

Δ = b² -4 .a . c  

Δ= (-4)² -4 . 9 . (-20)

Δ = 16 -36 . (-20)

Δ = 16 + 720

Δ = 736

736    |4

184    |4

46      |2

23      |23

1  

4² . 2 . 23

4² . 46

b)

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

5x - 15 - 2x - 4 = 3 - 5x

5x - 2x - 15 - 4 =- 5x + 3

3x - 19 = -5x + 3

3x + 5x = 3 + 19

8x = 22

x = 22/8

Explicação passo-a-passo: