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Find all real solutions of the equation.
x4/3 − 7x2/3 + 10 = 0

User AbiNerd
by
3.6k points

1 Answer

10 votes
Solve by Factoring x^(2/3)-7x^(1/3)+10=0
x
2
3

7
x
1
3
+
10
=
0
x
2
3
-
7
x
1
3
+
10
=
0
Rewrite
x
2
3
x
2
3
as
(
x
1
3
)
2
(
x
1
3
)
2
.
(
x
1
3
)
2

7
x
1
3
+
10
=
0
(
x
1
3
)
2
-
7
x
1
3
+
10
=
0
Let
u
=
x
1
3
u
=
x
1
3
. Substitute
u
u
for all occurrences of
x
1
3
x
1
3
.
u
2

7
u
+
10
=
0
User Vanagar
by
3.6k points