Question 178341
√(x+2) -x=0 b.∛x -5=3 c.X3/2 = 27
:
{{{sqrt(x+2) - x}}} = 0
:
{{{sqrt(x+2)}}} = x
square both sides and you have
x + 2 = x^2
A quadratic equation:
x^2 - x - 2 = 0
Factors to
(x-2)(x+1) = 0
two solutions
x = +2
x = -1
Check both solutions in original equation
{{{sqrt(2+2) - 2}}} = 0
and
{{{sqrt(-1+2) - (-1)}}} = 0
{{{sqrt(1) + 1}}} does not = 0
:
x = 2 is the only solution
:
:
∛x - 5 = 3 
:
∛x = 3 + 5
:
∛x = 8
x = 2
:
:
{{{x^(3/2)}}} = 27 
find the cube root of both sides
{{{x^(1/2)}}} = 3
which is:
{{{sqrt(x)}}} = 3
Square both sides
x = 9
:
:
Check on a good calc:
enter 9^(3/2) = 27