If `y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5,` then the value of `(a^2)/(b^2)` is_______

Explanation

`y=(a+bx^(3//2))/(x^(5//4))`
`"or "y'=((3)/(2)bx^(1//2)x^(5//4)-(5)/(4)x^(1//4)(a+bx^(3//2)))/(x^(5//2))`
According to the question,
`0=((3)/(2)b5^(1//2)5^(5//4)-(5)/(4)5^(1//4)(a+b5^(3//2)))/(5^(5//2))`
`"or "(3b)/(2)5^(7//4)-a(5^(5//4))/(4)-5b(5^(7//4))/(4)=0`
`"or "b5^(7//4)=a5^(5//4)`
`"or "bsqrt(5)=a`
`"or "a:b=sqrt(5):1`