Question

а+в-с=5
ав-вс-ас=-2
Найти а²+b²+c² -?

Answer 1

$a+b-c=5; ,; ; ab-bc-ac=-2; ,; ; a^2+b^2+c^2=?\\(a+b-c)^2=25; ;\\(a+b-c)^2=Big ((a+b)-cBig )^2=(a+b)^2-2(a+b)c+c^2=\\=a^2+2ab+b^2-2ac-2bc+c^2=a^2+b^2+c^2+2(ab-ac-bc); ;\\a^2+b^2+c^2+2(underbrace {ab-bc-ac}_{-2})=25\\a^2+b^2+c^2-4=25\\a^2+b^2+c^2=29$