Question

Determinati numerele a si b stiind ca $a^{2}$ - $b^{2}$ =40 si a+b=10

Answer 1

$a^{2}- b^{2} = 40$
(a+b)(a-b)=40
10(a-b)=40 => a-b=40/10=4

Fac sistem si obtin : $\left \{ {{a+b=10} \atop {a-b=4}} \right.$
Adun ecuatiile si obtin ca: 
2a=14=>a=7
a+b=10=>b=10-a=10-7=3

Asadar $\left \{ {a=7} \atop {b=3}} \right.$