Question

Задание на фотографии. С ПОЯСНЕНИЕМ, даю 25 БАЛОВ

Answer 1

$x-\dfrac{1}{x}=5\\\\\Big(x-\dfrac{1}{x}\Big)^{2} =5^{2}\\\\x^{2} -2\cdot x\cdot\dfrac{1}{x} +\dfrac{1}{x^{2} }=25\\\\x^{2} -2+\dfrac{1}{x^{2} } =25\\\\x^{2}+\dfrac{1}{x^{2} }=27 \\\\\Big(x^{2}+\dfrac{1}{x^{2} }\Big)^{2} =27^{2}\\\\x^{4}+2\cdot x^{2} \cdot \dfrac{1}{x^{2} }+\dfrac{1}{x^{4} }= 729\\\\x^{4} +2+\dfrac{1}{x^{4} } =729\\\\\boxed{x^{4}+\dfrac{1}{x^{4} }=727}$