Question

Resolva as equações: a) (3\2)x²+(7\3)x=0 b)2x²-8x=0 c)5x²-20=0 d)2x²-800=0 e)(√3\2)x²-(√5\√3)x=0 ============================================================= Um retângulo tem comprimento medindo ( x + 3 ) e largura (x + 4) . Qual a expressão que representa a área desse retângulo? *

Answer 1

Explicação passo-a-passo:

1.

a) $\sf \dfrac{3}{2}x^2+\dfrac{7}{3}x=0$

$\sf 9x^2+14x=0$

$\sf x\cdot(9x+14)=0$

$\sf x'=0$

$\sf 9x+14=0~\longrightarrow~9x=-14~\longrightarrow~x"=\dfrac{-14}{9}$

$\sf S=\left\{\dfrac{-14}{9},0\right\}$

b) $\sf 2x^2-8x=0$

$\sf 2x\cdot(x-4)=0$

$\sf 2x=0~\longrightarrow~x'=0$

$\sf x-4=0~\longrightarrow~x"=4$

$\sf S=\{0,4\}$

c) $\sf 5x^2-20=0$

$\sf 5x^2=20$

$\sf x^2=\dfrac{20}{5}$

$\sf x^2=4$

$\sf x=\pm\sqrt{4}$

$\sf x'=2$

$\sf x=-2$

$\sf S=\{-2,2\}$

d) $\sf 2x^2-800=0$

$\sf 2x^2=800$

$\sf x^2=\dfrac{800}{2}$

$\sf x^2=400$

$\sf x=\pm\sqrt{400}$

$\sf x'=20$

$\sf x=-20$

$\sf S=\{-20,20\}$

e) $\sf \dfrac{\sqrt{3}}{2}x^2-\dfrac{\sqrt{5}}{\sqrt{3}}x=0$

$\sf \dfrac{\sqrt{3}}{2}x^2-\dfrac{\sqrt{15}}{3}x=0$

$\sf 3\sqrt{3}x^2-2\sqrt{15}x=0$

$\sf x\cdot(3\sqrt{3}x-2\sqrt{15})=0$

$\sf x'=0$

$\sf 3\sqrt{3}x-2\sqrt{15}=0$

$\sf 3\sqrt{3}x=2\sqrt{15}$

$\sf x=\dfrac{2\sqrt{15}}{3\sqrt{3}}$

$\sf x"=\dfrac{2\sqrt{5}}{3}$

$\sf S=\left\{0,\dfrac{2\sqrt{5}}{3}\right\}$

2. $\sf S=comprimento\cdot largura$

$\sf S=(x+3)\cdot(x+4)$

$\sf S=x^2+4x+3x+12$

$\sf S=x^2+7x+12$

Answer 2

Vamos lá :

a)

(3\2)x² + (7\3)x = 0   . 6

3.3.x² + 7.2.x = 0

9x² + 14x = 0

x(9x + 14) = 0

x₁ = 0  ; x₂ = - 14/9

b)

2x² - 8x = 0

2x(x - 4) = 0

x₁ = 0 ; x₂ = 4

c)

5x² - 20 = 0  : 5

x² - 4 = 0

x² - 2² = 0

(x + 2)(x - 2) = 0

x₁ = - 2 ; x₂ = 2

d)

2x² - 800 = 0   : 2

x² - 400 = 0

x² - 20² = 0

(x + 20)(x - 20) = 0

x₁ = - 20 ; x₂ = 20

e)

(√3\2)x² - (√5\√3)x = 0  

(√3/2)x² - (√5.√3/3)x = 0 . 6

(3√3)x² - (2.√5.√3)x = 0

(√3 . x)(3x - 2√5) = 0

x₁ = 0 ; x₂ = 2√5/3

2)

Ar = (x + 3)(x + 4)

Ar = x² + 4x + 3x + 12

Ar = x² + 7x + 12

Espero ter ajudado !!