Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
729 views
in Linear Inequations by (23.5k points)
closed by

What values of x satisfy \(x^{\frac23}+x^{\frac13}\) – 2 < 0?

(a) – 8 < x <

(b) – 8 < x <

(c) – 1 < x <

(d) 1 < x < 8

1 Answer

+1 vote
by (24.0k points)
selected by
 
Best answer

(a) – 8 < x < 1

\(x^{\frac23}+x^{\frac13}\) – 2 <

⇒ y2 + y – 2 < 0, where y = \(x^{\frac13}\) 

⇒ (y – 1) (y + 2) <

⇒ (y – 1) < 0, (y + 2) > 0 or (y – 1) > 0, (y + 2) <

⇒ y < 1, y > – 2 or y > 1, y < – 2 

⇒ – 2 < y <

⇒ – 2 < \(x^{\frac13}\) <

– 8 < x < 1.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...