Question

Реши систему уравнений методом алгебраического сложения:

{d2+c2=61
{d2−c2=11

1.{d1=
{c1=
2.{d2=
{c2=−
3.{d3=−
{c3=
4.{d4=−
{c4=−

Answer 1

$\displaystyle \left \{ {{d^2+c^2=61} \atop {d^2-c^2=11}} \right. +\\\\\left \{ {2d^2+c^2-c^2=61+11=2\cdot 6^2} \atop {c^2=61-d^2\qquad \qquad \qquad \qquad}} \right.$

d² = 6²

c² = 61-36 = 5²

1. $\displaystyle \left \{ {{d_1=6} \atop {c_1=5}} \right.$

2. $\displaystyle \left \{ {{d_2=6\; \; \;} \atop {c_2=-5}} \right.$

3. $\displaystyle \left \{ {{d_3=-6} \atop {c_3=5\; \; \;}} \right.$

4. $\displaystyle \left \{ {{d_4=-6} \atop {c_4=-5}} \right.$