Question 99213
I've seen the problem up here several times, and I believe, like me, the tutors have found that there is no solution to this problem, so have passed it by.
:
Assume you mean:
{{{sqrt(x)- 2 = 6sqrt(x^3- 26)}}}
:
Square both sides, gets rid of the radical on the left and square 6
{{{(sqrt(x)- 2)^2 = 36(x^3- 26)}}}
:
FOIL the left side, multiply what's inside brackets on the right
{{{x - 2sqrt(x) - 2sqrt(x) + 4}}} = 36x^3 - 936
:
{{{x - 4sqrt(x) + 4}}} = 36x^3 - 936
:
{{{-4sqrt(x)}}} = 36x^3 - x - 936 - 4
:
{{{-4sqrt(x)}}} = 36x^3 - x - 940
:
At this point we should square both sides again, a real tedious operation.
Before I attempted this I entered y = {{{sqrt(x)-6sqrt(x^3- 26)- 2}}} into to my TI83 and found it had no real roots. (did not cross the x axis)
:
Are you sure this problem has been copied down correctly?