Question

Hallar el valor de ∛x , si: 1+3+5....+(2x +5)= 900

Answer 1

Respuesta:

3

Explicación paso a paso:

1 + 3 + 5 .... + (2*x + 5) = 900

Se trata de una progresión aritmética:

an = a1 + (n-1)*r

2*x + 5 = 1 + (n-1)*(2)

2*x + 4 =(n-1)*(2)

x + 2 = n - 1

x + 3 = n

Entonces la suma sera:

S = (a1 + an)*n/2

900 = [1 + (2*x + 5) ]*(x + 3)/2

900*2 = [1 + (2*x + 5) ]*(x + 3)

1800 = (2*x + 6)*(x + 3)

1800 = 2*(x + 3)*(x + 3)

1800 = 2*(x + 3)^2

900 = (x + 3)^2

30 = (x + 3)

30 - 3 = x

27 = x

Hallando:

= ∛x

= ∛27

= 3