the following equation has no root . find the relationship between a , b , c : 1: c≤2 2: c >2 3: c >ab 4: c≤ ab eq^n : (√( x+1+b +2(√(x+b)) )) + (√(x+1+a +2(√(x+a)))) = c


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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


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