12) this one is frm Arthur Engel....hain na....seen this one bfor...somebody asked on aops.
1 > Solve the following equation for " x " -
16 x 6 - 24 x 4 + 10 x 2 - 1 = 18 x
2 > The positive reals " x " , " y " , " z " satisfy the following equation -
x 2 + x y + y 23 = 25
y 23 + z 2 = 9
z 2 + z x + x 2 = 16
Find : - x y + 2 y z + 3 z x
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UP 0 DOWN 0 0 4
4 Answers
1
341Hint for 1:
Write the equation as (4x3-3x)2-(1-x2) = 1/(8x). Ring any bells?
1Alternate hint for 1 :
The L.H.S , after factorising becomes , ( 2 x 2 - 1 ) ( 8 x 4 - 8 x 2 + 1 ) . Ring any bells : ) ?
Hint for 2 :
Geometry is a powerful tool .
1for 2nd one can think eqs in terms of cosine rule and pythagorean triples.