Question

Se 80 + y = y √3

Qual o valor de y?!

Quero o desenvolvimento do cálculo, por favor!
Obrigada desde já! ^^ 

Answer 1

80+y = y\/3
(80+y)² = (y\/3)²
6400+160y+y² = 3y²
3y²-y²-160y-6400=0
2y²-160y-6400=0 (:2)
y²-80y-3200=0
delta = 6400+12800
delta = 19200
19200|2
09600|2
04800|2
02400|2
01200|2
00600|2
00300|2
00150|2
00075|3
00025|5
00005|5
00001
= 2^8 x 3 x 5²
\/2^8x3x5² = 
2^4x5\/3 =
80\/3
y = -(-80)+/-80\/3/ 2
y = (80+/-80\/3)/2
y = 40+/-40\/3
y' = 40-40\/3 = 40(1-\/3)
y" = 40+40\/3 = 40(1+\/3)

Answer 2

$80+y=y\sqrt{3}\\\\y\sqrt{3}-y=80\\\\y(\sqrt{3}-1)=80\\\\y=\frac{80}{\sqrt{3}-1}\\\\y=\frac{80}{\sqrt{3}-1}\times\frac{\sqrt{3}+1}{\sqrt{3}+1}\\\\y=\frac{80(\sqrt{3}+1)}{3-1}\\\\y=\frac{80(\sqrt{3}+1)}{2}\\\\\boxed{y=40(\sqrt{3}+1)}$