Question Number 149041 by mathdanisur last updated on 02/Aug/21

(√(x - 3 + 2(√(x - 4)))) − (√(x + 5 - 6(√(x - 2)))) =2 ⇒ x = ?

Commented bybramlexs22 last updated on 02/Aug/21

Commented byMJS_new last updated on 02/Aug/21

your picture is not enough. do they intersect at x≈4.5 or not? also there might be an intersection for x≥13+6(√2)

Commented bybramlexs22 last updated on 02/Aug/21

the curve y=(√(x−3+2(√(x−4)) ))−(√(x+5−6(√(x−2)))) and the line y=2 does not intersection

Answered by MJS_new last updated on 02/Aug/21

f_1 (x)=(√(x−3+2(√(x−4)))) defined for x≥4 strictly increasing for x≥4 f_2 (x)=(√(x+5−6(√(x−2)))) defined for 2≤x≤13−6(√2) ∨ x≥13+6(√2) strictly decreasing for 2≤x≤13−6(√2) strictly increasing for x≥13+6(√2) for 4≤x≤13−6(√2) the maximum of f_1 (x)−f_2 (x)=(√(10−6(√2)−2(√3)−2(√6)))≈1.72<2 ⇒ no solution for x≥13+2(√6): 4<f_1 (x)−f_2 (x)≤(√(10+6(√2)+2(√3)+2(√6)))≈5.18 ⇒ no solution