If k R is such that the equation 2 ^2 x=3 x+k has no real solution, then which of the following is correct?

Step-by-step solution

Given, 2 ^2 x-3 x-k=0 has no real solution. ^2 x- ^2 x=1 ^2 x=1+ ^2 x Then, 2 (1+ ^2 x )-3 x-k=0 2 ^2 x-3 x+(2-k)=0 Above equation has no real solution. D < 0 9 ^2 x-4(2-k) (2 ^2 x ) < 0 ^2 x(9-16+8 k) < 0 8 k-7 < 0 k < 7 / 8