One of the roots of the equation `2000x^6 + 100x^5 + 10x^3 + x-2 =0` is of the form `(m+sqrt(n))/ (r )` , where m is non zero integer and n and r are relatively prime natural numbers. Find the value of `m + n + r` .

One of the roots of the equation 2000x^6 +100x^5 +10x^3+x-2=0 is the form (sqrt(m)-n))/( r) , where m is non zero integer and n and r are relatively prime natural numbers. Find the value of m+n+r .

One of the roots of the equation 2000x^(6)+100x^(5)+10x^(3)+x-2=0 is of the form (m+sqrt(n))/(r), when m29. is non zero integer and and r are relatively prime natural numbers.Find the value of m+n+r

One of the roots of the equation 54x^(6)+27x^(5)+9x^(3)+3x=2(x^(2)!=(1)/(3)) is form (-sqrt(m)+-sqrt(n))/(sqrt(3).r) where m non zero integer and n and r are co-prime to each other,then the value of (m+n).r is equal to

x^(m)xx x^(n)=x^(m+n) , where x is a non zero rational number and m,n are positive integers.

If x be any non zero integer and m, n be negative integers. Then x^(m)xxx^(n) is equal to

Let f(x)=x^((m)/(n)) for x in R where m and n are integers,m even and n odd and '0

If the area enclosed by the curve y^(2)=4x and 16y^(2)=5(x-1)^(3) can be expressed in the form (L sqrt(M))/(N) where L and N are relatively prime and M is a prime, find the value of (L+M+N) .

If the acute angle between the tangents drawn from (0,1) to the graph of f(x)=x^(3)-3x^(2)+3x is tan^(-1)((m)/(n)) where m, n are relatively prime natural numbers. Then the value of m+n is

S={(x,y)|x,y in R,x^(2)+y^(2)-10x+16=0} The largest value of (y)/(x) can be put in the form of (m)/(n) where m,n are relatively prime natural numbers,then m^(2)+n^(2)=