Home » Inequality » Inequality Question : Find the minimum value possible

Inequality Question : Find the minimum value possible

Q.)P,Q and R are distinct natural numbers:
If V = \frac { { P(Q }^{ 2 }+{ R }^{ 2 })+Q(P^{ 2 }+{ R }^{ 2 })+R(P^{ 2 }+{ R }^{ 2 }) }{ PQR } , V must be
i)Greater than 5
ii)Greater than 6
iii)Greater than 4
=>V = \frac { { P(Q }^{ 2 }+{ R }^{ 2 })+Q(P^{ 2 }+{ R }^{ 2 })+R(P^{ 2 }+{ R }^{ 2 }) }{ PQR }
= (\frac { Q }{ R } +\frac { R }{ Q } )+(\frac { P }{ R } +\frac { R }{ P } )+(\frac { P }{ Q } +\frac { Q }{ P } )

From A.M > G.M (Equality is not included because all numbers are distinct)
\frac { Q }{ R } +\frac { R }{ Q } ) > 2 as P,Q and R are distinct natural numbers.
Similarly for others.
Hence V > 6.


6 Comments

  1. binary trading

    […]that will be the end of this report. Right here you’ll find some internet sites that we consider you will value, just click the links over[…]

  2. all forex brokers

    […]Here is a good Weblog You may Uncover Intriguing that we Encourage You[…]

  3. free bonus no deposit

    […]check below, are some entirely unrelated web sites to ours, however, they are most trustworthy sources that we use[…]

  4. forex trading

    […]Sites of interest we have a link to[…]

  5. Barcode kaufen

    […]here are some links to sites that we link to since we think they may be worth visiting[…]

  6. 他媽的 says:

    …Recommended websites

    […]Excellent blog here! Also your site so much up fast![…]

Leave a comment