Solution: Solve $ 3^k - rac3^2k2 < -1 $. Let $ x = 3^k $ (note $ x > 0 $). The inequality becomes $ x - racx^22 < -1 $, or $ -racx^22 + x + 1 < 0 $. Multiply by $-2$ (reversing inequality): $ x^2 - 2x - 2 > 0 $. Solve $ x^2 - 2x - 2 = 0 $: roots are $ x = 1 \pm \sqrt3 $. Since $ x > 0 $, critical point is $ x = 1 + \sqrt3 pprox 2.732 $. The quadratic is positive when $ x > 1 + \sqrt3 $. Since $ x = 3^k $, find smallest $ k $ such that $ 3^k > 1 + \sqrt3 $. Test $ k = 1 $: $ 3^1 = 3 > 2.732 $. Check $ R(1) = 3 - rac92 = -1.5 < -1 $. Thus, $ k = oxed1 $. - Nelissen Grade advocaten