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```				   if a,b,c are distinct positive numbers , then the expression (b+c-a)(c+a-b)(a+b-c)-abc is positive or negative........?
```

6 years ago

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```										Dear nishant
let x ,y,z are three positive number
so use AM ≥GM
x+y ≥2(xy)1/2
y+z ≥2(yz)1/2
z+x ≥2(zx)1/2

so (x+y)(y+z)(z+x)≥2(xy)1/22(yz)1/22(zx)1/2
or (x+y)(y+z)(z+x)≥8(xyz)
now put x=b+c-a
y= c+a-b
z= a+b-c
or x+y =2c  , y+z =2a , z+x =2b
(2c)(2a)(2b)    ≥8(b+c-a )( c+a-b)( a+b-c)
abc      ≥(b+c-a )( c+a-b)( a+b-c)
(b+c-a )( c+a-b)( a+b-c) -abc ≤ 0

Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin
```
6 years ago

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