arcsin(x^2 -3) = arcsin(x^2 +3x+4) find x=?


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Question Number 146545 by mathdanisur last updated on 13/Jul/21

$a r c s i n (x^{2} - 3) = a r c s i n (x^{2} + 3 x + 4)$ $f i n d x = ?$
	Answered by Olaf_Thorendsen last updated on 14/Jul/21
	$arcsin(x^2 −3) = arcsin(x^2 +3x+4) ⇔ { ((−1≤x^2 −3≤+1)),((−1≤x^2 +3x+4≤+1 (1))),((x^2 −3 = x^2 +3x+4)) :} (1) : impossible because min_R (x^2 +3x+4) = (7/4) ⇒ S = ∅$
	$\arcsin (x^{2} - 3) = \arcsin (x^{2} + 3 x + 4)$ $\Leftrightarrow {\begin{cases} - 1 ⩽ x^{2} - 3 ⩽ + 1 \\ - 1 ⩽ x^{2} + 3 x + 4 ⩽ + 1 (1) \\ x^{2} - 3 = x^{2} + 3 x + 4 \end{cases}$ $(1) : impossible because \min_{R} (x^{2} + 3 x + 4) = \frac{7}{4}$ $\Rightarrow S = \emptyset$
	Commented by mathdanisur last updated on 14/Jul/21

	$t h a n k y o u S e r c o o l$
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