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```
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

```
4 years ago Ashutosh Mohan Sharma
180 Points
```							(x-y)2>=0; Therefore, x2+y2>=2xt>=0Also using Nima J's proof, it follows that(X2-y2)2>=0; Therefore, x4+y4>=2x2y2Dividing both sides by 2 gives(a) ½(x2+y2)>=xy and(b) ½(x4+y4)>=x2y2Now since (x2+y2)>=2xy; it follows that(x2+y2)(z2+w2)>=(2xy)(2zw)=4xyzwTherefore, multiplying the factors gives:(c) x2z2+x2w2+y2z2+y2w2>=4xyzwNowX4+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
```
4 years ago
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