Question

What is the solution to the equation shown below

Answer 1

Plug values in!
3/(3-2) + 6 = sqrt(3-2) + 8
3 + 6 = 1 + 8
9=9 so the first one

Answer 2

x = 3

Option 1 is correct.

Explanation:

Given:
`(3)/(x-2)+6=√(x-2)+8`

First we check restriction on x from equation.

Denominator can't be 0

So, x-2 ≠0

x ≠ 2

Inside the square root value always positive.

Therefore, x-2 ≥ 0

x ≥ 2

Now simplify the equation.

`(3)/(x-2)+6=√(x-2)+8`

`(3)/(x-2)-2=√(x-2)`

squaring both sides

`((3)/(x-2)-2)^2=(√(x-2))^2`

`(9)/((x-2)^2)+4-(12)/(x-2)=x-2`

`9+4(x-2)^2-12(x-2)=(x-2)^3`

`9+4x^2+16-16x-12x+24=x^3-8-6x^2+12x`

`x^3-10x^2+40x-57=0`

`(x-3)(x^2-7x+19)=0`

x=3 and two are imaginary

Now we take intersection of all two condition and one solution.

x ≠ 2 and x ≥ 2 and x=3

Intersection of all three, x = 3

Hence, The solution of the given equation is 3