Question

решить систему уравнений

Answer 1

2х-у=13
х²-у²=23
$y = 2x - 13$
${x}^{2} - {y}^{2} = 23$
x²-(2x-13)²=23
x²-4x²+52x-169-23=0
-3x²+52x-192=0
3x²-52x+192=0

D1=(b/2)²-ac
D1=26²-192×3=100=10²
$x1 = \frac{26 + 10}{3} = \frac{36}{3} = 12 \\ x2 = \frac{26 - 10}{3} = \frac{16}{3}$

y1 = 2 × 12 - 13 = 11
y2 = 2 × 16/3 - 13 = 32/3 - 39/3 = -7/3