Question

What is the answer to v+2/v + 4/3 v = 11

Answer 1

v+2/v+4/(3v)=11, multiply through by 3v:

3v²+6+4=33v,

3v²-33v=-10,

v²-11v=-10/3,

v²-11v+121/4=121/4-10/3,

(v-11/2)²=(363-40)/12=323/12,

v-11/2=±√(323/12), v=11/2±5.1881 approx.

v=10.6881 or 0.3119.

Another interpretation: v+2/v+(4/3)v=11, multiply through by v:

v²+2+(4/3)v²=11v,

(7/3)v²-11v+2=0,

7v²-33v+6=0,

v=(33±√(1089-168))/14=4.5249 or 0.1894 approx.