Let the maximum value of expression `y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(3) -1) ` for `x gt 1 is (p)/(1),` where p and 1q are relatively prime natural numbers, then `p+ q=`

Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(3) -1) for x gt 1 is (p)/(q), where p and q are relatively prime natural numbers, then p+ q=

The value of sum_(n=1)^(oo)(1)/((3n-2)(3n+1)) is equal to (p)/(q), where p and q are relatively prime natural numbers.Then the value of (p^(2)+q^(2)) is equal to

If the ratio of the coefficient of x^(10) in (1-x^(2))^(10) and term independent of x in (x-2/x)^(10) is p/q (where p and q are relative prime numbers) then q/8-p is

Let d bet the minimum value of f(x)=5x^(2)-2x+(26)/(5) and f(x) is symmetric about x=r. If sum_(n=1)^(n=1)(1+(n-1)d)r^(n-1) equals,(p)/(q), where p and q are relative prime,then find the value of (3q-p).

Let (x,y) be a pair of real number satisfying 56x+33y=-(y)/(x^(2)+y^(2)) and 33x-56y=(x)/(x^(2)+y^(2)) . If x/y=(p)/(q) (where p and q are relatively prime and pgtq ) then (6p-q) is

If the value of lim_(x->0)( ((3/ x)+1)/((3/x)-1))^(1/x) can be expressed in the form of e^(p/q), where p and q are relative prime then find the value of (p+q) .