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Hanoi Open Mathematics Competition
2012 Hanoi Open Mathematics Competitions
10
10
Part of
2012 Hanoi Open Mathematics Competitions
Problems
(2)
Q10 - Hanoi Open Mathematical Olympiad 2012 - Junior Section
Source:
6/10/2012
Q10. Solve the following equation
1
(
x
+
29
)
2
+
1
(
x
+
30
)
2
=
13
36
.
\frac{1}{(x+29)^2}+ \frac{1}{(x+30)^2}= \frac{13}{36}.
(
x
+
29
)
2
1
+
(
x
+
30
)
2
1
=
36
13
.
Compute The values
Source:
1/24/2016
Suppose that the equation
x
3
x^3
x
3
+p
x
2
x^2
x
2
+qx+1 = 0; with p; q are rational numbers, has 3 real roots
x
1
x_1
x
1
;
x
2
x_2
x
2
;
x
3
x_3
x
3
; where
x
3
=
2
+
5
x_3 = 2 +\sqrt{5}
x
3
=
2
+
5
; compute the values of p and q?