Question-173652

Question Number 173652 by saly last updated on 15/Jul/22

Commented by saly last updated on 15/Jul/22

H e l p m e

Commented by JDamian last updated on 15/Jul/22

y o u r e a l l y n e e d h e l p - h a v e y o u m i s s e d a n y t e r m ?

Commented by saly last updated on 15/Jul/22

l o g \sqrt{\frac{2022}{x^{3} + x + 2}}

Answered by okbruh123 last updated on 15/Jul/22

f i r s t o f a l l, t h e r e s n o b a s e m e n t i o n e d .

s o i a m a s s u m i n g i t s c o m m o n l o g

s i n c e b a s e > 0 a n d \neq 1, w e n e e d n o t w o r r y a b o u t i t .

\Rightarrow \sqrt{\frac{2022}{x^{3} + x + 2}} > 0 \cap x^{3} + x + 2 \neq 0

\Rightarrow a s s q u a r e r o o t i s a l w a y s ⩾ 0 a n d i n t h i s c a s e a l s o \neq 0

\Rightarrow x \in R \cap (x + 1) + x^{3} + 1 \neq 0

\Rightarrow x \in R \cap (x + 1) + (x + 1) (x^{2} + 1 - x) \neq 0

\Rightarrow R \cap (x + 1) (x^{2} - x + 2) \neq 0 \Rightarrow x \neq - 1

\Rightarrow x \in R - {- 1}

t h i s w a s d o m a i n .

i l l a n s w e r r a n g e s e p a r a t e l y