x2 +1 14. If х *+13 3 } and x > 1; find (i) x-? (ii) r3 X- بابک х x
Answers
Answer:
Ifx2+1/x2−7 find the valve of x3+1/33
Given equation is x2+1/x2=7
we know that(x+1/x)2=x2+2.x.1/x+(1/x)2
=x2+2+1/x2
=(x2+1/x2)+2
=7+2
=9.
∴(x+1/x)2=9
⇒(x+1/x)=(3)x
⇒(x+1/x)=3.
Now ,
(x3+1/x)3=(x+1/x)3−3.x.1/x.(x+1/x)
=(x+1/x)3−3(x+1/x)
=(3)3−3(3)
=27−9
=18.
Step-by-step explanation:
=3
3
1
=>x+
x
1
=
3
10
Squaring both sides,
(x+
x
1
)
2
=(
3
10
)
2
=>x
2
+(
x
1
)
2
+2(x)(
x
1
)=
9
100
=>x
2
+(
x
1
)
2
=
9
100
−2
=>x
2
+(
x
1
)
2
=
9
82
Now, (x−
x
1
)
2
=x
2
+(
x
1
)
2
−2(x)(
x
1
)
=(
9
82
−2)
=(
9
64
)
(x−
x
1
)=
(
9
64
)
=(
3
8
)
=2
3
2
Now, (x
3
−
x
3
1
)=(x−
x
1
)[(x
2
+(
x
1
)
2
+(x)(
x
1
)]
=(
3
8
)(
9
82
+1)
=(
3
8
)(
9
91
)
=
27
728
=26
7
26