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=

If 2009 = p^a x q^b where p and q are prime numbers, then the value of (p+q) is

Let lim _( x to oo) n ^((1)/(2 )(1+(1 )/(n))). (1 ^(1) . 2 ^(2) . 3 ^(3)....n ^(n ))^((1)/(n ^(2)))=e^((-p)/(q)) where p and q are relative prime positive integers. Find the value of |p+q|.

The radical centre of the three circles is at the origin. The equations of the two of the circles are x^(2)+y^(2)=1 and x^(2)+y^(2)+4x+4y-1=0 . If the third circle passes through the points (1, 1) and (-2, 1), and its radius can be expressed in the form of (p)/(q) , where p and q are relatively prime positive integers. Find the value of (p+q) .

Let x and y be the positive real numbers such that log_x y=-(1)/(4) , then value of the expression log_x(xy^5)-log_y""((x^(2))/(sqrt(y))) is (p)/(q) then q is _____________. { where p , q in N and are coprime to each other }

If the value of [sin(sin^(-1)(0. 5)+sin^(-1)(0. 4))] x [(sin(sin^(-1)(0. 5)-sin^(-1)(0. 4))] can be expressed as p/q (where p ,q in N are relatively prime), then ((q-p)/(13)) is

consider f(x)==cos^-1x+xos((sqrt3 x+sqrt(1-x^2))/2) , if sum_(r=1)^100 f(1-(1/10)^r)=p/q pi where p and q relatively prome number then find the value of p-16q

For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q > 0 are relatively prime integers 0 then which one does not hold good?

Let x,y and z are positive reals and x ^(2) + xy + y ^(2)=2,y ^(2)+yz+z ^(2) =1 and z ^(2) +zx+x^(2) =3. If the value of xy + zx can be expressed as sqrt((p)/(q)) where p and q are relatively prime positive integral find the value of p-q,

If the area bounded by y = ||x|^(2) - 4|x| + 3|| and the x-axis from x = 1 to x = 3 is p/q (where, p & q are coprime) then the value of p + q is