Question 95257
{{{((sqrt(7x-9))^(1/3))+(11)}}} = 14
:
Subtract 11 from both sides:
{{{((sqrt(7x-9))^(1/3)))}}} = 14 - 11
:
{{{((sqrt(7x-9))^(1/3)))}}} = 3
:
Cube both sides:
{{{((sqrt(7x-9))^(1/3))^3)}}} = {{{3^3}}}
:
That gives us;
{{{sqr(7x-9)}}} = 27
:
Square both sides and you have:
7x - 9 = 729
7x = 729 + 9
7x = 738
x = 738/7, a rather nasty fraction, but that is the solution
:
:
Check our solution:
Substitute for x in {{{sqrt(7(738/7) - 9)}}}
{{{sqrt(738 - 9)}}} = {{{sqrt(729)}}} = 27
Cube rt of 27 = 3, so we have 3 + 11 = 14