Question

Помогите пожалуйста 3 и 5 задание с подробным решением.

Answer 1

$(7^{frac{1}2}-3^{frac{1}2})^2+(7^{frac{1}2}+3^{frac{1}2})^2=(7^{frac{1}2})^2-2*7^{frac{1}2}*3^{frac{1}2}+(3^{frac{1}2})^2+(7^{frac{1}2})^2+\ +2*(7^{frac{1}2})^2*3^{frac{1}2}+(3^{frac{1}2})^2=7^1+3^1+7^1+3^1=7+3+7+3=20$

$big((sqrt[4]{a}-sqrt[4]{b})^{-2}+(sqrt[4]{a}+sqrt[4]{b})^{-2}big):frac{a^{frac{1}2}+b^{frac{1}2}}{a-b}=\ big(frac{1}{(a^{frac{1}4}-b^{frac{1}4})^2}+frac{1}{(a^{frac{1}4}+b^{frac{1}4})^{2}}big):frac{sqrt a+sqrt b}{(sqrt a-sqrt b)(sqrt a+sqrt b)}=\ big(frac{1}{(a^{frac{1}4}-b^{frac{1}4})^2}+frac{1}{(a^{frac{1}4}+b^{frac{1}4})^{2}}big):frac{1}{sqrt a-sqrt b}=$
$big(frac{sqrt a-sqrt b}{(a^{frac{1}4}-b^{frac{1}4})^2}+frac{sqrt a-sqrt b}{(a^{frac{1}4}+b^{frac{1}4})^{2}}big)=\ big(frac{a^{frac{1}2}-b^{frac{1}2}}{(a^{frac{1}4}-b^{frac{1}4})^2}+frac{a^{frac{1}2}-b^{frac{1}2}}{(a^{frac{1}4}+b^{frac{1}4})^{2}}big)=\ big(frac{(a^{frac{1}4}-b^{frac{1}4})(a^{frac{1}4}+b^{frac{1}4})}{(a^{frac{1}4}-b^{frac{1}4})^2}+frac{(a^{frac{1}4}-b^{frac{1}4})(a^{frac{1}4}+b^{frac{1}4})}{(a^{frac{1}4}+b^{frac{1}4})^{2}}big)=$
$frac{a^{frac{1}4}+b^{frac{1}4}}{a^{frac{1}4}-b^{frac{1}4}}+frac{a^{frac{1}4}-b^{frac{1}4}}{a^{frac{1}4}+b^{frac{1}4}}=$
$frac{(a^{frac{1}4}+b^{frac{1}4})(a^{frac{1}4}+b^{frac{1}4})}{(a^{frac{1}4}-b^{frac{1}4})(a^{frac{1}4}+b^{frac{1}4})}+frac{(a^{frac{1}4}-b^{frac{1}4})(a^{frac{1}4}-b^{frac{1}4})}{(a^{frac{1}4}+b^{frac{1}4})(a^{frac{1}4}-b^{frac{1}4})}=\ frac{(a^{frac{1}4}+b^{frac{1}4})^2+(a^{frac{1}4}-b^{frac{1}4})^2}{a^{frac{1}2}-b^{frac{1}2}}=frac{a^{frac{1}2}+2a^{frac{1}4}b^{frac{1}4}+b^{frac{1}2}+a^{frac{1}2}-2a^{frac{1}4}b^{frac{1}4}+b^{frac{1}2}}{a^{frac{1}2}-b^{frac{1}2}}=$
$=frac{a^{frac{1}2}+2a^{frac{1}4}b^{frac{1}4}+b^{frac{1}2}+a^{frac{1}2}-2a^{frac{1}4}b^{frac{1}4}+b^{frac{1}2}}{a^{frac{1}2}-b^{frac{1}2}}=\ =frac{2a^{frac{1}2}+2b^{frac{1}2}}{a^{frac{1}2}-b^{frac{1}2}}=frac{2(a^{frac{1}2}+b^{frac{1}2})(a^{frac{1}2}-b^{frac{1}2})}{(a^{frac{1}2}-b^{frac{1}2})^2}=frac{2(a-b)}{(a^{frac{1}2}-b^{frac{1}2})^2}$