Need help in to simplify and solve for Y?

Question

Sqrt(y+1)+sqrt(y-3)=5

I am trying to help my daughter in math and need help I can't remember how to do this and show the work getting there.

Answer 1

That looks particularly awful.

Normally when solving a radical equation you isolate the radical and square both sides, but that 5 is going to complicate matters.

sqrt(y + 1) + sqrt(y - 3) = 5

Subtract sqrt (y - 3) from both sides.
sqrt(y + 1) = 5 - sqrt(y - 3)

Square both sides (take care on the right side).
y + 1 = 25 - 10sqrt(y - 3) +(y - 3)

Combine like terms on the right side.
y + 1 = 22 - 10sqrt(y - 3) + y

Subtract y from both sides.
1 = 22 - 10sqrt(y - 3)

Add 10 sqrt(y - 3) and subtract one from both sides
10sqrt(y - 3) = 21

And square both sides again.
100(y - 3) = 441

Divide by 100
y - 3 = 4.41

Add 3 to both sides
y = 7.41

That was just ridiculous. Just to be on the safe side - check.

sqrt(7.41 + 1) + sqrt(7.41 - 3) = 5
sqrt(8.41) + sqrt(4.41) = 5
2.9 + 2.1 = 5
5 = 5

Answer 2

Sqrt(y+1) = (y+1)^(1/2)
Sqrt(y-3) = (y-3)^(1/2) .....^ means to the power of
laws of exponents say you can multiply them when two quantities of the same exponentiation are added:

((y+1)(y-3))^(1/2)=5
square both sides
(y+1)(y-3) = 25
y^2 - 3y +y -3 = 25
y^2 -2y -3 = 25

so you need to solve y^2 - 2y -28 = 0 using the quadratic formula

Answer 3

y+1+y-3=5
2y-2=5
2y=7
y=3.5


thats how i would do it! hope it helps.