x² – 10x + 1 = 0 find the value of x² + 1/x²
Answers
Answered by
0
Step-by-step explanation:
Explanation:
Isolate all terms involving
x
on one side and move the constant to the other side.
x
2
+
10
x
=
1
Now, the original quadratic,
x
2
+
10
x
−
1
,
is in the form
a
x
2
+
b
x
+
c
where
a
=
1
,
b
=
10
,
c
=
−
1
.
To complete the square, we first want to add
(
b
2
)
2
to each side.
(
b
2
)
2
=
(
10
2
)
2
=
5
2
=
25
, so we add
25
to each side.
x
2
+
10
x
+
25
=
1
+
25
The left side needs to be factored. Fortunately, since we added
(
b
2
)
2
to each side, the factored form will simply be
(
x
+
b
2
)
2
=
(
x
+
5
)
2
(
x
+
5
)
2
=
26
Now, take the root of both sides, accounting for positive and negative answers on the right.
√
(
x
+
5
)
2
=
±
√
26
x
+
5
=
±
√
26
Solving for
x
yields
x
=
±
√
26
−
5
Answer link
Answered by
0
Step-by-step explanation:
is it correct???
Attachments:
Similar questions