The number of all the possible integral values of n>2 such that 2 n + 2 n = n 2 is

Step-by-step solution

Given, 2 n + 2 n = n 2 Squaring both sides ( 2 n + 2 n )^2= n 4 gathered ^2 2 n + ^2 2 n +2 2 n 2 n = n 4 1+ n = n 4 n = n 4 -1 n = n-4 4 gathered As, n >0, n>2 So, n-4 4 >0 n>4 Also, ( 2 n )+ 2 n = 2 ( 4 + 2 n ) . From Eq. (i) 2 ( 4 + 2 n )= n 2 ( 4 + 2 n )= n 2 2 Since, ( 4 + 2 n ) 2 We get, n 2 2 < 1 n < 8 From Eqs. (ii) and (iii) 4 < n < 8 So, n=5,6,7 Hence, number of integral value of n is 3 .