Question

Помогите с решением

Answer 1

Ответ:

$ab\sqrt[\pi]{4}$

Объяснение:

$((a^{\pi}+b^{\pi})^{2}-(a^{\pi}-b^{\pi})^{2})^{\frac{1}{\pi}};$

$a^{2}-b^{2}=(a-b)(a+b);$

$((a^{\pi}+b^{\pi})^{2}-(a^{\pi}-b^{\pi})^{2})^{\frac{1}{\pi}}=(((a^{\pi}+b^{\pi})-(a^{\pi}-b^{\pi}))((a^{\pi}+b^{\pi})+(a^{\pi}-b^{\pi})))^{\frac{1}{\pi}}=$

$=((a^{\pi}+b^{\pi}-a^{\pi}+b^{\pi})(a^{\pi}+b^{\pi}+a^{\pi}-b^{\pi}))^{\frac{1}{\pi}}=(2b^{\pi} \cdot 2a^{\pi})^{\frac{1}{\pi}}=(4a^{\pi}b^{\pi})^{\frac{1}{\pi}}=$

$=4^{\frac{1}{\pi}} \cdot ((ab)^{\pi}})^{\frac{1}{\pi}}=ab \cdot \sqrt[\pi]{4}=ab\sqrt[\pi]{4};$