SOLUTION: {{{y=x*(9-2*x^2)^0.5}}} if y= 0 and x=a Find the value of a giving your answer as a multiple of {{{2^o.5}}} the answer it gives is {{{(3*2^0.5)/2}}} i keep trying this

Algebra ->  Radicals -> SOLUTION: {{{y=x*(9-2*x^2)^0.5}}} if y= 0 and x=a Find the value of a giving your answer as a multiple of {{{2^o.5}}} the answer it gives is {{{(3*2^0.5)/2}}} i keep trying this       Log On


   

Question 53340This question is from textbook MEI structured mathematics A2 Pure mathematics c3/c4
: y=x%2A%289-2%2Ax%5E2%29%5E0.5
if y= 0
and x=a
Find the value of a giving your answer as a multiple of 2%5Eo.5
the answer it gives is %283%2A2%5E0.5%29%2F2
i keep trying this problem but cant get anywhere near the answer it gives, and cant see where im going wrong.
i keep getting
2%5Eo.5%2F3 or 3%2F2%5E0.5
can you help? This question is from textbook MEI structured mathematics A2 Pure mathematics c3/c4

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+x%289-2x%5E2%29%5E%280.5%29 First, square both sides of the equation.
y%5E2+=+x%5E2%289-2x%5E2%29 Now substitute y = 0 and x = a.
0+=+a%5E2%289-a%5E2%29 Apply the zero product principle.
a%5E2+=+0 and/or 9-2a%5E2+=+0
9-2a%5E2+=+0 Subtract 9 from both sides.
-2a%5E2+=+-9 Divide both sides by -2.
a%5E2+=+9%2F2 Take the square root of both sides.
a+=+3%2F%282%29%5E%280.5%29 Finally, multiply numerator and denominator by 2%5E%280.5%29
a+=+%283%2A2%5E%280.5%29%29%2F2