Question 53340
{{{y = x(9-2x^2)^(0.5)}}} First, square both sides of the equation.
{{{y^2 = x^2(9-2x^2)}}} Now substitute y = 0 and x = a.
{{{0 = a^2(9-a^2)}}} Apply the zero product principle.
{{{a^2 = 0}}} and/or {{{9-2a^2 = 0}}}
{{{9-2a^2 = 0}}} Subtract 9 from both sides.
{{{-2a^2 = -9}}} Divide both sides by -2.
{{{a^2 = 9/2}}} Take the square root of both sides.
{{{a = 3/(2)^(0.5)}}} Finally, multiply numerator and denominator by {{{2^(0.5)}}}
{{{a = (3*2^(0.5))/2}}}