Question

5p) 4. Dacă 3⁸–3⁶ = x³", atunci:........​

Answer 1

Răspuns:

$\red{\boxed{x=18}}$

Explicație pas cu pas:

$3^8 - 3^6=x^3 \Rightarrow 3^6\Big(3^2 - 1 \Big) = x^3$

$3^6\Big( 9-1\Big) = x^3 \Rightarrow 3^6 \cdot 8 = x^3$

$\Big(3^2 \Big)^3 \cdot 2^3 =x^3 \Rightarrow 9^3 \cdot 2 ^3 = x^3$

$\Big(9 \cdot 2 \Big )^3 = x^3 \Rightarrow \red{ \boxed{x = 18}}$

Answer 2

$\bf {3}^{8} - {3}^{6} = {x}^{3}$

$\bf {3}^{6} \cdot \big( {3}^{8 - 6} - {3}^{6 - 6} \big) = {x}^{3}$

$\bf {3}^{6} \cdot \big( {3}^{2} - {3}^{0} \big) = {x}^{3}$

$\bf \big({3}^{2} \big)^{3} \cdot \big( 9 - 1 \big) = {x}^{3}$

$\bf 9^{3} \cdot 8 = {x}^{3}$

$\bf 9^{3} \cdot {2}^{3}= {x}^{3}$

$\bf \big(9\cdot {2} \big)^{3} = {x}^{3}$

$\bf 18^{3} = {x}^{3} \implies \red{ \underline{x = 18}}$

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