Question

система х^2+y^2=74.x-y=2

Answer 1

x=2+y

(2+y)^2+y^2=74

4+4y+y^2+y^2=74

2y^2+4y+4-74=0

y^2+2y-35=0

D/4=1+35=36

y1=-1+6=5

y2=-1-6=-7

 

y1=5

x1=7

 

y2=-7

x2=-5

Answer 2

x=2+y

(2+y)^2+y^2=74

4+4y+y^2+y^2=74

2y^2+4y+4-74=0

y^2+2y-35=0

D/4=1+35=36

y1=-1+6=5

y2=-1-6=-7

 

ответ: y1=5

          x1=7

 

         y2=-7

         x2=-5

Answer 3

$left {begin{array}{lcl} {{x^2 + y^2=74} \ {x - y = 2}} end{array}right. \\\left { begin{array}{lcl} {{x^2 + y^2 - 2xy + 2xy=74} \ {x-y=2}} end{array}right. \ \ \left {begin{array}{lcl} {{(x - y)^2 + 2xy=74} \ {x-y=2}} end{array}right. \ \\left {begin{array}{lcl} {{2xy=70} \ {x - y=2}} end{array}right.\\\left {begin{array}{lcl} {{y(y + 2)=35} \ {x=y + 2}} end{array}right.$

$\ \ left{begin{array}{lcl} {{y^2+2y-35=0} \ {x=y+2}}end{array}right.$

Решим квадратное уравнение y² + 2y - 35 = 0

По теореме Виета: $left {begin{array}{lcl} {{y_1 + y_2=-2} \ {y_1cdot y_2=-35}}end{array} right. Rightarrow ; left begin{array}{lcl} {{y_1=-7,; x_1 = -5} \ {y_2 = 5, ; x_2 = 7}}end{array} right.$

Ответ: (-5, -7) и (7, 5)