PMC Forum: MATHS

IF X+Y+Z = 8 ,THEN MINIMUM VALUE OF X²+Y²+Z²=

a. 153/7

b.125/6

c.83/4

d.64/3

please tell the answer in detail.

by SRINIVAS IYENGAR - Monday, 13 February 2006, 10:15 AM

Use

a.m>=g.m

X+Y+Z >= 3*(X*Y*Z)^1/3

AND

X²+Y²+Z²>=3*(X²*Y²*Z²)^1/3

we get answer as (D) 64/3

by Mohit Khandelwal - Monday, 13 February 2006, 12:19 PM

THANX SRINIVAS

by DIBYADARSHI MISHRA - Tuesday, 14 February 2006, 12:25 AM

THERE IS AN INEQUALITY RULE

RMS MEAN>=ARITHMETIC MEAN

i.e. SQRT((X^2+Y^2+Z^2)/3)>=(X+Y+Z)/3

PUTTING THE VALUES WE GET IT TO BE 64/3

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