arcsin-x-2-3-arcsin-x-2-3x-4-find-x-

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} + 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