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

( b + c )( c + a )( a + b ) is greater than


A

abc

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

2abc

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

4abc

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

8abc

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

8abc


Explanation for correct options:

Step 1: Declaring the theorem:

We know, A.M = a+b2

G.M = ab

For two positive numbers, A.M G.M

Step 2: Comparing the given equation with the theorem:

For the given problem,

a+b2ab.. (1)

b+c2bc.. (2)

a+c2ac.. (3)

Step 3: Solving the equations:

Now, multiplying equations (1, 2, 3),

a+b2×b+c2×a+c2ab×bc×ac

(a+b)(b+c)(a+c)8ab×bc×ac

(a+b)(b+c)(a+c)8a2×b2×c2

(a+b)(b+c)(a+c)8abc

(a+b)(b+c)(a+c)abc

Therefore, the expression (a+b)(b+c)(a+c) is greater than 8abc

Hence, Option (D) is correct.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adaptive Q28
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon