If x square+1/x square=7, find the value of x+1/x
Answers
Answered by
0
Answer:
Ifx
2
+1/x
2
−7 find the valve of x
3
+1/3
3
Given equation is x
2
+1/x
2
=7
we know that(x+1/x)
2
=x
2
+2.x.1/x+(1/x)
2
=x
2
+2+1/x
2
=(x
2
+1/x
2
)+2
=7+2
=9.
∴(x+1/x)
2
=9
⇒(x+1/x)=
(3)
x
⇒(x+1/x)=3.
Now ,
(x
3
+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.
∴x
3
+1/x
3
=18.
Similar questions