Consider the equation: k x+ 2 x=2 k-7 If the equation possesses solution, then what is the minimum value of k ?

Step-by-step solution

K x+ 2 x=2 K-7K x+ (1-2 ^2 x )=(2 K-7)2 ^2 x-K x+(2 K-8)=0 This is a quadratic equation in x . x= -(-K) K^2-4(2)(2 K-8) 2 2 For minimum value of K , x=-1 aligned & K K^2-16 K+64 4 =-1 & ( ) K^2-16 K+64 =-K-4 aligned Squaring both sides, we get aligned & K^2-16 K+64=K^2+16+8 K & 24 K=48 & K=2 aligned