Question

Сумма двух чисел равна 46, а сумма их квадратов равна 1130. Найдите эти числа

Answer 1

$left { {{x+y=46,} atop {x^2+y^2=1130;}} right. \ (x+y)^2=x^2+2xy+y^2, \ x^2+y^2=(x+y)^2-2xy=46^2-2xy=2116-2xy, \ left { {{x+y=46,} atop {2116-2xy=1130;}} right. left { {{y=46-x,} atop {986-2xy=0;}} right. left { {{y=46-x,} atop {493-x(46-x)=0;}} right. \ 493-46x+x^2=0, \ D_1=(-23)^2-493=36, \ x=23pm6, \ left [ {{x=29,} atop {x=17}} right. left [ {{y=17,} atop {y=29;}} right. \ (17;29) , (29;17).$