Răspuns:
Explicație pas cu pas:
Fie A ( 2 ; 3 ) si B ( 4 ; x ) . Determinati x € R , astfel incat AB = 2V5.
AB=√[(x2-x1)²+(y2-y1)²] ⇒2√5=√[(4-2)²+(x-3)²] ⇒2√5=√2²+(x-3)² ⇒20=4+(x-3)² ⇒16=x²-6x+9 ⇒x²-6x-7=0 ⇒
Δ=(-6)²-4·1·(-7)=36+28=64 ⇒√Δ=√64=8
X1,2=(6±8)/2 ⇒X1=(6+8)/2=7 X2=(6-8)/2=-1 X1=7 X2=-1
Proba: A(2;3) B(4;7) ⇒AB=√[(4-2)²+(7-3)²]=√(2²+4²)=√20=2√5
Proba: A(2;3) B(4;-1) ⇒AB=√[(4-2)²+(-1-3)²]=√[(2²+(-4)²]=√20=2√5
