Solve the problem:?

Question

radical sign over x+3 + radical sign over x-1 =2

Answer 1

Hi,

x = 1

Get a radical alone on one side first.

sqrt(x + 3) = 2 - sqrt(x - 1)

Now square both sides, not term by term, but by squaring the entire sides. that means you will have to "FOIL" the right side:

[sqrt(x + 3)] = [2 - sqrt(x - 1)]^2

x + 3 = 4 - 4sqrt(x - 1) + x - 1

Combine like terms.

0 = sqrt(x - 1)

Now square both sides again.

0 = x - 1

1 = x

Remember you always have to check your answers on these by plugging them back into the original equation, because sometimes there are extraneous solutions that don't work. In this case, x = 1 is OK.

I hope that helps!!

While Heather got the right answer, that method won't work on every problem...

Answer 2

square both sides of the equation to get
squaring a radical gets rid of the radical
x+3 + x-1 = 4 now simplify
2x+2=4
2x=2
x=1

Answer 3

squaring both sides,
2x + 2 + 2 * radical over(x+3)(x-1) = 4
or, x + 1 + rad over(x+3)(x-1) = 2
or, rad over(x+3)(x-1) = 1 - x
again, squaring:
2x - 3 = -2x + 1
or, 4x = 4
or, x = 1

Answer 4

sq.root of x+3 + sq.root of x-1 =2
Squaring both sides =
x+3 + x-1+2 *sqroot(x+3)(x-1) =4
2x+2 * sq root of(x+3)(x-1)=2
dividing through out by 2

x+sq root (x+3)(x-1) =2
Therefore,

sqroot of(x+3)(x-1)= 2-x

Squaring,

(x+3)(x-1)= (2-x)^2

X^2 + 2x-2 = 4-4x+x^2
x^2-x^2 + 2x+4x= 4+2
6x=6
x=1
the solution is x=1

Answer 5

(x+3)^.5 + (x-1)^.5 =2
(x+3)^.5 = 2 - (x-1)^.5
x+3 = 4 -4(x-1)^.5 +x-1
-4(x-1)^.5=0
16(x-1)= 0
x- 1=0 --> x = 1