If `a+b=1,a^(2)+b^(2)=2` and given that `a^(7)+b^7=(m)/(n)` where `m` & `n` are co-primes. Find `m+n`

If two positive integers m and n are expressible as as m = ab^(2) and n = a^(3) b , where a and b are prime numbers, then find LCM (m, n)

If vec A and vec B are two non-zero vectors such that |vec A+vec B|=(|vec A-vec B|)/(2) and |vec A|=2|vec B| then the angle between vec A and vec B is theta such that cos theta=-(m)/(n) (where m and n are positive integers and (m)/(n) lowest form then find m+n

If M(a, b)=a^(2)+b^(2)+ab,N(a, b)=a^(2)+b^(2)-ab . Find the value of M(7, N(9, 4)) .

lim_(x rarr0)((a^(x)+b^(x)+c^(x))/(3))^(2/x),(a>0,b>0,c>0) is (abc)^(m/n) then ((m+n))/(10) is : (where [ m,n in N and m&n are co-prime)

If A is a square matrix such that A^(2)=A then find the value of (m+n) if (I+A)^(3)-7A=mI+nA. (Where m and n are Constants)