If _r= | array ccc 1 & n & n 2 r & n^2+n+1 & n^2+n 2 r-1 & n^2 & n^2+n+1 array | and _ r=1 ^n _r=56 , then n is equal to

Step-by-step solution

Putting r=1,2,3, , n and using the formula aligned & 1=n & and r= n(n+1) 2 & (2 r-1)=1+3+5+ =n^2 & _ r=1 ^n _r= | array cc n & n n(n+1) & n^2+n+1 n^2 & n^2 array c array l n^2+n n^2+n+1 array |=56 aligned Applying C₁ C₁-C₃, C₂ C₂-C₃ , we get aligned & | array ccc 0 & 0 & n 0 & 1 & n^2+n -n-1 & -n-1 & n^2+n+1 array |=56 & & n(n+1)=56 & & n^2+n-56=0 aligned aligned & & (n+8)(n-7) & =0 & & n & =7,(n -8) aligned