Question Number 115268 by bobhans last updated on 24/Sep/20

(√(4^x −5.2^(x+1) +25)) +(√(9^x −2.3^(x+2) +17)) ≤ 2^x −5

Answered by john santu last updated on 24/Sep/20

(√(4^x −5.2^(x+1) +25)) +(√(9^x −2.3^(x+2) +17)) ≤ 2^x −5  note that 2^x −5 ≥ 0  ⇒(√((2^x −5)^2 ))+(√(9^x −18.3^x +17)) ≤2^x −5  ∣2^x −5∣ +(√(9^x −18.3^x +17)) ≤2^x −5  (√(9^x −18.3^x +17)) ≤ 0  let 3^x  = t ⇒t^2 −18.t+17 ≤ 0  (t−1)(t−17)≤ 0  ⇒ t=1 ∨t=17  ⇒3^x =1⇒x=0 (rejected)  ⇒3^x  = 17 ⇒x = ^3 log 17 (acceptable)