Verified answer

√(a-3)²+(2-1)²=√(a-2)²+(2-4)²

√a²-6a+9+1=√(a²-4a+4+4)

-6a+4a=8-10

-2a=-2

2a=2

a=1

Veja:

d(P,A)=d(P,B)

d(P,A)=√(3-a)²+(1-2)²

d(P,A)=√(9-6a+a²+1)

d(P,A)=√(a²-6a+10)

d(P,B)=√(2-a)²+(4-2)²

d(P,B)=√(4-4a+a²+4)

d(P,B)=√(a²-4a+8)

d(P,A)=d(P,B)

√(a²-6a+10)=√(a²-4a+8)

(√(a²-6a+10))²=(√(a²-4a+8))²

a²-6a+10=a²-4a+8

a²-6a-a²+4a=8-10

-2a=-2

a=-2/-2

a=1

A abscissa a do ponto P é igual a 1.