Question

if 5(x–1) +4=34,then 5x–5+4=34 or 5x =34+1.​

Answer 1

Let f(x)=3

Let f(x)=3 x−4

Let f(x)=3 x−4 +5

Let f(x)=3 x−4 +5 x−4

Let f(x)=3 x−4 +5 x−4 −34

Let f(x)=3 x−4 +5 x−4 −34f

Let f(x)=3 x−4 +5 x−4 −34f ′

Let f(x)=3 x−4 +5 x−4 −34f ′ (x)=3

Let f(x)=3 x−4 +5 x−4 −34f ′ (x)=3 x−4

Let f(x)=3 x−4 +5 x−4 −34f ′ (x)=3 x−4 ln3+5

Let f(x)=3 x−4 +5 x−4 −34f ′ (x)=3 x−4 ln3+5 x−4

Let f(x)=3 x−4 +5 x−4 −34f ′ (x)=3 x−4 ln3+5 x−4 ln5>0∀x∈R

Let f(x)=3 x−4 +5 x−4 −34f ′ (x)=3 x−4 ln3+5 x−4 ln5>0∀x∈RThus f is strictly increasing function, so it will have maximum one real root.

Let f(x)=3 x−4 +5 x−4 −34f ′ (x)=3 x−4 ln3+5 x−4 ln5>0∀x∈RThus f is strictly increasing function, so it will have maximum one real root.It can be observed that x=6 is satisfying above equation.

Let f(x)=3 x−4 +5 x−4 −34f ′ (x)=3 x−4 ln3+5 x−4 ln5>0∀x∈RThus f is strictly increasing function, so it will have maximum one real root.It can be observed that x=6 is satisfying above equation.Hence x=6 is the only root of the given equation.