wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If (a,b,c)+R such that b+ca,c+ab,a+bc are positive, then the expression
(b+ca)(a+bc)(c+ab)abc is

A
Positive
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Negative
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Zero
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of the above.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B Negative
we know that A.M.G.M.

x+y2xy

let x=b+ca and y=a+bc

therefore, b+ca+a+bc2(b+ca)(a+bc)

2b2(b+ca)(a+bc)

b(b+ca)(a+bc) ----------(1)

similarly, let x=b+ca and y=c+ab

therefore, b+ca+c+ab2(b+ca)(c+ab)

2c2(b+ca)(c+ab)

c(b+ca)(c+ab) ----------(2)

similarly, let x=a+bc and y=c+ab

therefore, a+bc+c+ab2(a+bc)(c+ab)

2a2(a+bc)(c+ab)

a(a+bc)(c+ab) ----------(3)

multiplying (1), (2), (3) we get

abc(b+ca)2(a+bc)2(c+ab)2

abc(b+ca)(a+bc)(c+ab)

(b+ca)(a+bc)(c+ab)abc

(b+ca)(a+bc)(c+ab)abc0

therefore, (b+ca)(a+bc)(c+ab)abc is negative

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Animal Tissues
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon