If a^2 - 4a - 1 = 0, find the value of a^2 + 1/a^2 + 3a - 3/a
Answers
Answered by
1
Answer:
.
24+3root5.
30a 2 −4a−1=0
⇒
a
a
2
−1
=4⇒a−
a
1
=4
Now, a
2
+3a+
a
2
1
=
a
3
=a
2
+
a
2
1
+3(a−
a
1
)=(a−
a
1
)
2
+2+3(a−
a
1
)
=4
2
+2+3×4=30.
Answered by
2
Answer:
30
Step-by-step explanation:
a^2 - 4a - 1 = 0
= (a^2 - 1)/a
= a - 1/a
= 4
Now, a^2 + 3a + 1/a^2 = 3/a
= a^2 + 1/a^2 + 3(a - 1/a)
= (a - 1/a)^2 + 2 + 3(a - 1/a)
= 4^2 + 2 + 3 ×4
= 30
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