If `^(n+2)C_8:^(n-2)P_4=57:16`, then prove that n=19.

If G.M. of a and b is (a^n+b^n)/(a^(n-1)+b^(n-1)) then prove that n=1/2 .

If G.M. of a and b is (a^(n+1)+b^(n+1))/(a^n+b^n) ,then prove that n=-1/2 .

If .^(m+n)P_2=72 and .^(m-n)P_2=6 ,then find the values of m and n.

If A=[(a,b),(0,1)] , where a ne 1 , then prove that A^(n) =[(a^(n), (b(a^(n)-1))/(a-1)),(0,1)], n in N .

If A and G be the A.M. and G.M. of two numbers a and b and A:G=m:n ,then prove that- a:b=m+sqrt(m^2-n^2) :m-sqrt(m^2-n^2)

If A and B are two finite sets,then prove that n(A uu B)=n(A)+n(B)-n(AnnB)

If A=[(3,-4),(1,-1)] , prove by induction that A_n=[(1+2n,-4n),(n,1-2n)],n in N

If cos A+sin B=m and Sin A+cos B=n ,then prove that 2sin (A+B)=m^2+n^2-2 .

If (n in N) then applying division algorithm prove that each of the following in an integer (n(4n^2-1))/3

If tantheta +sintheta=m and tantheta-sintheta=n prove that m^2-n^2=4sqrt(mn)