From the information given below, what is the value of #p^3 + q^4 + r^5# ?

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Answer 1 · 2017-11-24T20:02:55

#3#

From

#27pqr ge (p+g+r)^3# we conclude that

#root(3)(pqr) ge 1/3(p+q+r)# but for #{p,q,r} in RR^+# we have also

#1/3(p+q+r) ge root(3)(p q r) rArr 1/3(p+q+r) = root(3)(p q r) #

We have also

#(3p+4q+5r)/12 ge root(12)(p^3q^4r^5) rArr le 1# then assuming

#root(12)(p^3q^4r^5) = 1 rArr p=q=r=1 rArr p^3+q^4+r^5 = 3#

NOTE

We have also

#p^3+q^4+r^5 ge 3 root(3)(p^3q^4r^5)#