Question

Zadanie 1

Rozwiaz rownanie

Zadanie 2

W ciagu geometrycznym trzeci wyraz ciagu jest wiekszy od pierwszego o 8, a czwarty od drugiego o 24. Znajdz te wyrazy ciagu

Answer 1

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

x^2 - 7 = -5

x^2 - 7 + 5 = 0

x^2 - 2 = 0

(x - √2)(x +√2) = 0

x = √2 lub x = -√2

 

2.

x ; y ; x + 8 ; y + 24

 

y / x = (x + 8) /  y

(x + 8) / y = (y + 24) / (x  +8)

 

y^2 = x(x + 8)

(x + 8)^2 = y^2 + 24y

 

y^2 = x^2 + 8x

x^2 + 16x + 64 = y^2 + 24y

 

y^2 = x^2 + 8x

x^2 + 16x + 64 = x^2 + 8x + 24y

 

y^2 = x^2 + 8x

8x + 64 = 24y

 

y^2 = x^2 + 8x

x + 8 = 3y

 

y^2 = x^2 + 8x

x = 3y - 8

 

y^2 = (3y - 8)^2 + 8(3y - 8)

y^2 = 9y^2 - 48y + 64 + 24y - 64

-8y^2 + 24y = 0

y^2 - 3y = 0

y(y - 3) = 0

y1 = 0 ∉ D

y2 = 3

 

y = 3

x  = 3*3 - 8 = 9 - 8 = 1

 

x = 1

y = 3