Question

alculati X astfel 3^ 37-27^12=2 × 81^10:x^2​

Answer 1

$\displaystyle{ 3^{37} - 27^{12} = 2 \cdot 81^{10} : x^{2} }$

$\displaystyle{ 3^{37} - (3^{3})^{12} = 2 \cdot (3^{4})^{10} : x^{2} }$

$\displaystyle{ 3^{37} - 3^{36} = 2 \cdot 3^{40} : x^{2} }$

$\displaystyle{ x^{2} = 2 \cdot 3^{40} : (3^{37} - 3^{36}) }$

$\displaystyle{ x^{2} = 2 \cdot 3^{40} : 3^{36} \cdot (3 - 1) }$

$\displaystyle{ x^{2} = 2 \cdot 3^{40-36} \cdot 2 }$

$\displaystyle{ x^{2} = 2 \cdot 3^{4} \cdot 2 }$

$\displaystyle{ x^{2} = 4 \cdot 81 }$

$\displaystyle{ x = \sqrt{4} \cdot \sqrt{81} }$

$\displaystyle{ x = 2 \cdot 9 }$

$\boxed{x=18}$