Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

JEE Class main Answered

a,b,c>0 then prove that a³+b³+c³+ab²+bc²+ca² >= 2(a²b+b²c+c²a)
question image
Asked by narender111reddy | 16 Apr, 2020, 15:46: PM
answered-by-expert Expert Answer
Given: a,b,c>0 
To prove: a³+b³+c³+ab²+bc²+ca² >= 2(a²b+b²c+c²a)
C o n s i d e r a cubed plus b cubed plus c cubed plus a b squared plus b c squared plus c a squared minus 2 open parentheses a squared b plus b squared c plus c squared a close parentheses equals a cubed plus b cubed plus c cubed plus a b squared plus b c squared plus c a squared minus 2 a squared b minus 2 b squared c minus 2 c squared a equals a cubed plus b cubed plus c cubed minus a squared b minus b squared c minus c squared a plus a b squared plus b c squared plus c a squared minus a squared b minus b squared c minus c squared a equals a squared open parentheses a minus b close parentheses plus b squared open parentheses b minus c close parentheses plus c squared open parentheses c minus a close parentheses plus a b open parentheses b minus a close parentheses plus b c open parentheses c minus b close parentheses plus c a open parentheses a minus c close parentheses equals a squared open parentheses a minus b close parentheses plus b squared open parentheses b minus c close parentheses plus c squared open parentheses c minus a close parentheses minus a b open parentheses a minus b close parentheses minus b c open parentheses b minus c close parentheses minus c a open parentheses c minus a close parentheses equals a squared open parentheses a minus b close parentheses minus a b open parentheses a minus b close parentheses plus b squared open parentheses b minus c close parentheses minus b c open parentheses b minus c close parentheses plus c squared open parentheses c minus a close parentheses minus c a open parentheses c minus a close parentheses equals a open parentheses a minus b close parentheses open parentheses a minus b close parentheses plus b open parentheses b minus c close parentheses open parentheses b minus c close parentheses plus c open parentheses c minus a close parentheses open parentheses c minus a close parentheses equals a open parentheses a minus b close parentheses squared plus b open parentheses b minus c close parentheses squared plus c open parentheses c minus a close parentheses squared subscript blank open parentheses a minus b close parentheses squared comma space open parentheses b minus c close parentheses squared space a n d space open parentheses c minus a close parentheses squared space w i l l space a l w a y s space b e space greater or equal than 0 space S i n c e comma space a comma space b comma space c greater than 0 rightwards double arrow a open parentheses a minus b close parentheses squared plus b open parentheses b minus c close parentheses squared plus c open parentheses c minus a close parentheses squared greater or equal than 0 T h u s comma space a cubed plus b cubed plus c cubed plus a b squared plus b c squared plus c a squared minus 2 open parentheses a squared b plus b squared c plus c squared a close parentheses greater or equal than 0 H e n c e comma space a cubed plus b cubed plus c cubed plus a b squared plus b c squared plus c a squared greater or equal than 2 open parentheses a squared b plus b squared c plus c squared a close parentheses
Answered by Renu Varma | 20 Apr, 2020, 12:33: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
JEE main - Maths
The number of ways in which at least one coin can be selected from 3 coins of one rupee, 4 coins of fifty paise, 5 coins of twenty paise and 6 coins of ten paise is-
Asked by kanishthkumawat | 29 Nov, 2024, 00:23: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
what is range of tan^-1 x
Asked by pawandhayal125 | 06 Oct, 2024, 10:03: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
what is 2+2
Asked by srishtipra2008 | 28 Sep, 2024, 10:33: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
n arithmetic means are inserted between the numbers 7 and 49. if the sum of these means is 364 then the sum of their squares is
Asked by yogeshsoni575 | 23 Sep, 2024, 23:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
consider a dodecagon then number of ways of selecting two triangles which can be made using the vertices of dodecagon so that they do not have a common side.
Asked by sumit.parsudih | 17 Sep, 2024, 22:22: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
the sum of infinite series 1/2(1/3+1/4)-1/4(1/3^2+1/4^2)+1/6(1/3^3+1/4^3)+
Asked by pritamlovevanshi5 | 15 Sep, 2024, 08:24: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
solve the equation 6x-y+3z=10 , 3x+6y=18 , x+y+5z=-10 by jacobis method with (3,0,-2) as the initial approcimate to the solution
Asked by ganeshbabugottapu7 | 12 Sep, 2024, 18:19: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
find the inverse of a Matrix by using gauss Jordan method -2. 1. 3 A = 0. -1. 1 1. 2. 0
Asked by ganeshbabugottapu7 | 10 Sep, 2024, 07:32: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
The sum of the reciprocals of the ages of two colleagues is nine times the difference of the reciprocals of their ages. If the ratio of the products of their ages to the sum of their ages is 100 : 9. Find their ages ?
Asked by parvatijaiswal9 | 17 Aug, 2024, 21:10: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
the equation of the plane (1,1,1) and (1,-1,-1) and perpendicular to 2x-y+z+5=0 is
Asked by ayushapatill2407 | 09 Aug, 2024, 19:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt