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
1.7k views
in Mathematics by (65.8k points)

If (x + y + z)3 = (y + z - x)3 + (z + x - y)3 + (x + y - z)3 + kxyz find the numerical value of k. Deduce the following result.

If a= 2015, b = 2014, c = 1/2014 prove that

(a + b +c)3 – (a + b - c)3 – (b + c – a)3 –(c + a – b)3 – 23 abc = 2015

1 Answer

+1 vote
by (71.2k points)
selected by
 
Best answer

(x + y + x)3 = (y + 2 – x)3 + (2 + x – y)3 + (x + y – 2)3 + kxyz

we see that by putting x = 0, the expression vanishes.

so x is a factor of the expression similarly y,z are factors of that expression.

The given expression is of 3rd degree & the factors so far obtained are also of 3rd degree hence if there is any constant factors supposing it to be k.

Then in order to find k

put x = 1, y = 1, z = 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.

Categories

...