Question

Equação Irracional[tex] \sqrt{y} -1 + 3 = y

Answer 1

$\sqrt{y-1} +3=y \\ \\ \sqrt{y-1} =y-3 \\ \\ ( \sqrt{y-1} )^2=(y-3)^2 \\ \\ y-1=y^2-6y+9 \\ \\ y^2-6y-y+9+1=0 \\ \\ y^2-7y+10=0$

a=1
b=-7
c=10

Δ=b²-4ac
Δ=(-7)²-4(1)(10)
Δ=49-40
Δ=9

y=(-b±√Δ)/2a=(7±√9)/2=(7±3)/2

y'=(7+3)/2=10/2=5
y"=(7-3)/2=4/2=2

verificação
para  y=5

$\sqrt{5-1} +3=5 \\ \sqrt{4} +3=5 \\ 2+3=5 \\ 5=5~~(V) \\ \\ para~~y=2 \\ \\ \sqrt{2-1} +3=2 \\ \sqrt{1} +3=2 \\ 1+3=2 \\ 4 \neq 2~~(F) \\ \\ S=\{5\}$