Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If for some
p
,
q
,
r
∈
R
p, q, r \in R
p
,
q
,
r
∈
R
, not all have same sign, one of the roots of the equation
(
p
2
+
q
2
)
x
2
−
2
q
(
p
+
r
)
x
+
q
2
+
r
2
=
0
(p^2 + q^2)x^2 - 2q(p + r)x + q^2 + r^2 = 0
(
p
2
+
q
2
)
x
2
−
2
q
(
p
+
r
)
x
+
q
2
+
r
2
=
0
is also a root of the equation
x
2
+
2
x
−
8
=
0
x^2 + 2x - 8 = 0
x
2
+
2
x
−
8
=
0
, then
q
2
+
r
2
p
2
\frac{q^2 + r^2}{p^2}
p
2
q
2
+
r
2
is equal to \_\_\_\_.
Browse the problem library