Question

3:5 totul la 1-x plus 3:5 totul la 1+x =1.2

Answer 1

Explicație pas cu pas:

$\bigg( \dfrac{3}{5} \bigg)^{1-x} + \bigg(\dfrac{3}{5}\bigg)^{1+x} = 1,2$

$\dfrac{3}{5}\bigg( \dfrac{3}{5} \bigg)^{-x} + \dfrac{3}{5}\bigg(\dfrac{3}{5}\bigg)^{x} = \dfrac{6}{5}$

$\bigg( \dfrac{3}{5} \bigg)^{-x} + \bigg(\dfrac{3}{5}\bigg)^{x} = 2$

$\bigg(\dfrac{3}{5}\bigg)^{x} = t$

${t}^{-1} + t - 2 = 0 \\ {t}^{2} - 2t + 1 = 0$

${(t - 1)}^{2} = 0 \implies t = 1$

$\bigg(\dfrac{3}{5}\bigg)^{x} = 1 \iff \bigg(\dfrac{3}{5}\bigg)^{x} = \bigg(\dfrac{3}{5}\bigg)^{0}$

$\implies \bf x = 0$

Answer 2

Răspuns:

x = 0

Explicație pas cu pas:

(3/5) * (3/5)^(-x) + (3/5) * (3/5)^x = 1,2

Fie (3/5)^x = y

3/5  /  y   +   3/5 * y = 1,2

3/5 y^2  -  1,2 y  +  3/5 = 0

Δ = 1,44 - 4*9/25 = 144/100 - 144/100 = 0

y1,2 = 1,2  /   6/5 ) = 1,2 / 1,2 = 1

(3/5)^x = 1

x = 0.