Question

3. Решите систему уравнений: x²+y² = 29 x+y=7​

Answer 1

Ответ:

${x}^{2} + {y}^{2} = 29 \\ x + y = 7$

$x = 7 - y \\ {(7 - y)}^{2} + {y}^{2} = 29$

$49 - 14y + {y}^{2} + {y}^{2} = 29 \\ 2 {y}^{2} - 14y + 20 = 0 \\ {y}^{2} - 7y + 10 = 0 \\ \\ y1 + y2 = 7 \\ y1 \times y2 = 10 \\ \\ y1 = 5 \\ y2 = 2$

$x1 = 7 - 5 = 2 \\ x2 = 7 - 2 = 5$

Answer 2

Ответ:

X²+y²=29

X+y=7

X²+y²=29

X=7-y

(7-y)²+y²=29

x=7-y

49-14y+y²+y²=29

x=7-y

2y²-14y+49-29=0

x=7-y

2y²-14y+20=0

x=7-y

Y²-7y+10=0

x=7-y

Y²-7y+10=0

D=49-40=9

Y1=(7+3)/2=5

Y2=(7-3)/2=2

X1=7-5=2

X2=7-2=5