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
69 views
in Algebra by (238k points)
closed by
If a + b + c = 3 and a2 + b2 + c2 = 25, then the value of the expression a3 + b3 + c3 – 3abc?
1. 93
2. 95
3. 99
4. 90

1 Answer

0 votes
by (240k points)
selected by
 
Best answer
Correct Answer - Option 3 : 99

Given:

a + b + c = 3

a2 + b2 + c2 = 25

Formula used:

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

a3 + b3 + c3 – 3abc = (a + b + c)[a2 + b2 + c2 – (ab + bc + ca)]

Calculation:

∵ (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

⇒ (3)2 = 25 + 2(ab + bc + ca)

⇒ 9 = 25 + 2(ab + bc + ca)

⇒ 9 -25 = 2(ab + bc + ca)

⇒ (-16) = 2(ab + bc + ca)

⇒ (ab + bc + ca) = (-16)/2 = (-8)

∴ a3 + b3 + c3 – 3abc = 3 × (25 + 8)

= 3 × 33

= 99

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.

...