Question

a ² + b ² = 676
a+b= 34​

Answer 1

Ответ: (24;10),  (10;24).

Объяснение:

$\displaystyle\\\left \{ {{a^2+b^2=676} \atop {a+b=34}} \right. \ \ \ \ \left \{ {{a^2+b^2+2ab=676+2ab} \atop {x=2}} \right. \ \ \ \ \ \left \{ {{(a+b)^2=676+2ab} \atop {a+b=34}} \right. \\\\\\\left \{ {{34^2=676+2ab} \atop {a+b=34}} \right. \ \ \ \ \left \{ {1156=676+2ab} \atop {a+b=34}} \right. \ \ \ \ \left \{ {{480=2ab\ |:2} \atop {a+b=34}} \right. \ \ \ \ \left \{ {{ab=240} \atop {a+b=34}} \right.$

$\displaystyle\\\left \{ {{a*(34-a)=240} \atop {b=34-a}} \right. \ \ \ \ \left \{ {{34a-a^2=240} \atop {b=34-a}} \right. \ \ \ \ \left \{ {{a^2-34a+240=0} \atop {b=34-a}} \right. \\\\\\\left \{ {{a^2-24b-10a+240=0} \atop {b=34-a}} \right. \ \ \ \ \left \{ {{a*(a-24)-10*(a-24)=0} \atop {b=34-a}} \right. \\\\\\\left \{ {{(a-24)(a-10)=0} \atop {b=34-a}} \right.\ \ \ \ \left \{ {{a_1=24\ \ \ \ a_2=10} \atop {b_1=10\ \ \ \ b_2=24}} \right. .$