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_______

Options

A. ` sqrt(5) : 1`
B. `5 : 2`
C. `3 : 5`
D. `1: 2 `

Answer

A

Explanation

` because y= (a + bx^(3//2))/(x^(5//4))`
On differentiating both sides w.r.t.x, we get
`y'=((x^((5)/(4)))((3)/(2) bx^((1)/(2))) - (5)/(4) (a + bx^(3//2))x^(1//4))/((x^(5//4))^(2))`
` because y' = 0 at x = 5 `
` therefore (3)/(c) bx^(7//4) - (5)/(4) (a + bx^(3//2)) x^^(1//4) = 0 , at x = 5 `
` rArr 6bx^(3//2) - 5 (a + bx^(3//2)) = 0 , at x = 5 `
` rArr bx^(3//2)= 5a , at x = 5 `
`rArr b(5)^(3//2) = 5a `
`rArr (a)/(b) = (5^(3//2) )/(5)`
`rArr a : b = sqrt(5): 1`