the-following-equation-has-no-root-find-the-relationship-between-a-b-c-1-c-2-2-c-gt-2-3-c-gt-ab-4-c-ab-eq-n-x-1-b-2-x-b-x-1-a-2-

Question Number 212550 by mnjuly1970 last updated on 17/Oct/24

t h e f o l l o w i n g e q u a t i o n h a s

n o r o o t . f i n d t h e r e l a t i o n s h i p

b e t w e e n a, b, c :

1 : c ⩽ 2

2 : c > 2

3 : c > a b

4 : c ⩽ a b

{e q}^{n} : \sqrt{x + 1 + b + 2 \sqrt{x + b}} + \sqrt{x + 1 + a + 2 \sqrt{x + a}} = c

Answered by Ghisom last updated on 17/Oct/24

x + 1 + α + 2 \sqrt{x + α} = {(1 + \sqrt{x + α})}^{2}

solving in R \Rightarrow \sqrt{x + α} ⩾ 0

\sqrt{x + a} + \sqrt{x + b} = c - 2

c - 2 > 0 \Rightarrow c > 2

Commented by mnjuly1970 last updated on 17/Oct/24