Question

o triplo do quadrado de um número é 472 qual é esse número?



Encontre incorreta ((Com contas por favor))
a) 2x^2=18x
b) x (x+3)=5x
c) 2x^2-6x= 0
D)x^2-x
e) -6x=4x-2x^2
f) 2x2=-5x^2-14x
​

Answer 1

1.

Seja "x" o numero procurado, temos:

--> Quadrado do numero:  x²

--> Triplo do quadrado do numero:  3x²

--> Triplo do quadrado do numero é igual a 472:  3x² = 472

Resolvendo a equação:

$3x^2~=~472\\\\\\x^2~=~\frac{472}{3}\\\\\\\boxed{x~=~\pm\sqrt{\frac{472}{3}}}$

2.

a)

$2x^2~=~18x\\\\\\2x^2-18x~=~0\\\\\\x^2-9x~=~0\\\\\\x.(x-9)~=~0\\\\\\\boxed{x~=~0}\\\\\\(x-9)~=~0\\\\\boxed{x~=~9}$

b)

$x.(x+3)~=~5x\\\\\\x^2+3x-5x~=~0\\\\\\x^2-2x~=~0\\\\\\x.(x-2)~=~0\\\\\\\boxed{x~=~0}\\\\\\(x-2)~=~0\\\\\\\boxed{x~=~2}$

c)

$2x^2-6x~=~0\\\\\\x^2-3x~=~0\\\\\\x.(x-3)~=~0\\\\\\\boxed{x~=~0}\\\\\\(x-3)~=~0\\\\\\\boxed{x~=~3}$

d)

Questão incompleta

e)

$-6x~=~4x-2x^2\\\\\\2x^2-6x-4x~=~0\\\\\\2x^2-10x~=~0\\\\\\x^2-5x~=~0\\\\\\x.(x-5)~=~0\\\\\\\boxed{x~=~0}\\\\\\(x-5)~=~0\\\\\\\boxed{x~=~5}$

f)

$2x^2~=~-5x^2-14x\\\\\\2x^2+5x^2+14x~=~0\\\\\\7x^2+14x~=~0\\\\\\x^2+2x~=~0\\\\\\x.(x+2)~=~0\\\\\\\boxed{x~=~0}\\\\\\(x+2)~=~0\\\\\\\boxed{x~=~-2}$