Question

Find the value of the following​

Answer 1

110.01 (aprox)

Explanation:

x + (1/x) = 5

x(x + (1/x)) = x(5)

x*x + x*1/x = 5x

x² + 1 = 5x

x² - 5x + 1 = 0

x = {-(-5)±√((-5²) -(4*1*1))} / (2*1)

x = {5±√(25-4)} / 2

x = {5±√21} / 2

x = {5±4.5826} / 2

x₁ = {5-4.5826} / 2 = 0.4174/2 = 0.2087

x₂ = {5+4.5826) / 2 = 9.5826/2 = 4.7913

Comprobación:

x₁

0.2087 + 1/0.2087 = 5

0.2087 + 4.7913 = 5

x₂

4.7913 + 1/4.7913 = 5

4.7913 + 0.2087 = 5

Respuesta:

x₁

(0.2087)³ + 1/(0.2087)³ = 0.0091 + 1/0.0091 = 0.0091 + 110.0101 = 110.019

x₂

(4.7913)³ + 1(4.7913)³ = 110 + 1/110 = 110 + 0.01 = 110.01