Question

найдите x в квадрате + y в квадрате если x+y = 7 и x y =3

Answer 1

$left { {{x+y=7} atop {xy=3}} right. = textgreater left { {{x=7-y} atop {(7-y)*y=3}} right. \(7-y)y=3\7y-y^2=3\y^2-7y+3=0\D=(-7)^2-4*1*3=49-12=37\y_1= frac{7+ sqrt{37} }{2};; ; ; ; y_2= frac{7- sqrt{37} }{2}\x_1= 7-y_1=7-frac{7+ sqrt{37} }{2}= frac{14-7- sqrt{37} }{2}= frac{7- sqrt{37} }{2}\\x_2= 7-y_2=7-frac{7- sqrt{37} }{2}= frac{14-7+ sqrt{37} }{2}= frac{7+ sqrt{37} }{2} \\x_1^2+y_1^2= (frac{7- sqrt{37} }{2})^2+(frac{7+ sqrt{37} }{2})^2= frac{49+37-14 sqrt{37}+49+37+14 sqrt{37} }{4}= frac{172}{4}=43\\x_2^2+y_2^2= (frac{7+ sqrt{37} }{2})^2+(frac{7- sqrt{37} }{2})^2= frac{49+37+14 sqrt{37}+49+37-14 sqrt{37} }{4}= frac{172}{4}=43\\x^2+y^2=43$