Giải phương trình
\[\dfrac{{16}}{{\sqrt {x - 6} }} + \dfrac{4}{{\sqrt {x - 2} }} + \dfrac{{256}}{{\sqrt {z - 1750} }} + \sqrt {x - 6} + \sqrt {x - 2} + \sqrt {z - 1750}=44\]
#1
Posted 09-10-2011 - 10:39
Zaraki
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PQT
Discovery is a child’s privilege. I mean the small child, the child who is not afraid to be wrong, to look silly, to not be serious, and to act differently from everyone else. He is also not afraid that the things he is interested in are in bad taste or turn out to be different from his expectations, from what they should be, or rather he is not afraid of what they actually are. He ignores the silent and flawless consensus that is part of the air we breathe – the consensus of all the people who are, or are reputed to be, reasonable.
Grothendieck, Récoltes et Semailles (“Crops and Seeds”).
#2
Posted 09-10-2011 - 10:48
soros_fighter
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Hạ sĩ
Áp dụng AM-GM:
Giải phương trình
\[\dfrac{{16}}{{\sqrt {x - 6} }} + \dfrac{4}{{\sqrt {x - 2} }} + \dfrac{{256}}{{\sqrt {z - 1750} }} + \sqrt {x - 6} + \sqrt {x - 2} + \sqrt {z - 1750}=44\]
$\dfrac{{16}}{{\sqrt {x - 6} }}+\sqrt {x - 6}\geq 8 $
$\dfrac{4}{{\sqrt {x - 2} }}+\sqrt {x - 2}\geq 4$
$\dfrac{{256}}{{\sqrt {z - 1750} }} + \sqrt {z - 1750}\geq 32$
Cộng vế theo vế ta có $VT \geq VP$
Đẳng thức xảy ra khi $x=22 ; y=6 ; z=2006$
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#3
Posted 09-10-2011 - 10:51
phuonganh_lms
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Đây là giải pt 2 ẩn $x,z$ hả Toàn?
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