Найдите | a+b | , если |a|=5 |b|=7 и |a-b|= [latex] \sqrt{84} [/latex]

[latex](a-b)^2=a^2-2ab+b^2=|a|^2-2|a||b|cos(a, b)+|b|^2=|a-b|^2[/latex] [latex]5^2-2*5*7*cos (a, b)+7^2=(\sqrt{84})^2[/latex] [latex]25-70cos(a,b)+49=84[/latex] [latex]cos(ab)=\frac{84-25-49}{70}=\frac{10}{-70}=-\frac{1}{7}[/latex] [latex]|a+b|=\sqrt{|a+b|^2}=\sqrt{(a+b)^2}=\sqrt{a^2+2ab+b^2}=[/latex] [latex]=\sqrt{|a|^2+2|a||b|cos(a,b)+|b|^2}=\sqrt{5^2+2*5*7*(-\frac{1}{7})+7^2}=[/latex] [latex]=\sqrt{25-10+49}=\sqrt{64}=8[/latex] ответ: 8