Question

Fie A(2;3) si B(4;x) . Determinati x ce apartine R , astfel incat AB = 2√5

Answer 1

Distanta de la A la B este:
√[(4 - 2)² + (x - 3)²] = 2√5
√[2² + (x - 3)²] = 2√5  ridicam ecuatia la puterea a doua:

4 + (x - 3)² = 4 * 5
(x - 3)²  = 20 - 4 
(x - 3)² = 16
x - 3 = √16
x - 3 = 4
x = 4 + 3
x = 7

Verificare:
√[(4 - 2)² + (7 - 3)²] = √[4 + 16] = √20 = √(4 * 5) = 2√5