if x+y+z = 0 then x 2 y 2 +y 2 z 2 +x 2 z 2 / x 4 +y 4 +z 4 = , Answer given was ½ but how it came tell please

Question

if x+y+z = 0 then x 2 y 2 +y 2 z 2 +x 2 z 2 / x 4 +y 4 +z 4 = , Answer given was ½ but how it came tell please

Ashutosh Mohan Sharma · Answer

(x-y)2>=0; Therefore, x2+y2>=2xt>=0
Also using Nima J's proof, it follows that
(X2-y2)2>=0; Therefore, x4+y4>=2x2y2
Dividing both sides by 2 gives
(a) ½(x2+y2)>=xy and
(b) ½(x4+y4)>=x2y2

Now since (x2+y2)>=2xy; it follows that
(x2+y2)(z2+w2)>=(2xy)(2zw)=4xyzw
Therefore, multiplying the factors gives:
(c) x2z2+x2w2+y2z2+y2w2>=4xyzw

Now
X4+y4+z4+w4 =
½[(x4+z4)+ (x4+w4)+ (y4+z4)+ (y4+w4)]>=
[(x2z2)+ (x2w2)+ (y2z2)+ (y2w2)]>= 4xyzw; equations (b) &(c)
Therefore,
X4+y4+z4+w4>=4xyzw

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

if x+y+z = 0 then x 2 y 2 +y 2 z 2 +x 2 z 2 / x 4 +y 4 +z 4 = , Answer given was ½ but how it came tell please

if x+y+z = 0 then x²y²+y²z²+x²z²/ x⁴+y⁴+z⁴ = ,
Answer given was ½ but how it came tell please

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on 9 grade maths

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

IIT JEE Courses

One Year IIT Programme

Two Year IIT Programme

Crash Course

NEET Courses

One Year NEET Programme

Two Year NEET Programme

One to One

School Board

Live Online classes

Class 11 & 12

Class 9 & 10

Class 6, 7 & 8

Test Series

JEE test series

NEET test series

C.B.S.E test series

Complete Self Study Packages

FULL COURSE

For class 12th

For class 11th

if x+y+z = 0 then x 2 y 2 +y 2 z 2 +x 2 z 2 / x 4 +y 4 +z 4 = , Answer given was ½ but how it came tell please

if x+y+z = 0 then x2y2+y2z2+x2z2/ x4+y4+z4 = ,Answer given was ½ but how it came tell please

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on 9 grade maths

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

if x+y+z = 0 then x²y²+y²z²+x²z²/ x⁴+y⁴+z⁴ = ,
Answer given was ½ but how it came tell please