CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If x+1x=5, then the sum of the digits of x9+1x9 is

A
18
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
24
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
20
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
30
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 20
Given: x+1x=5
Cubing both sides, we get:
(x+1x)3=53
x3+1x3+3x×1x(x+1x)=125

[ (x+y)3=x3+y3+3xy(x+y)]
x3+1x3+3(x+1x)=125
(x3+1x3)+3×5=125
(x+1x=5)
(x3+1x3)=110
Again, cubing both sides, we get:
(x3+1x3)3=(110)3
x9+1x9+3x3×1x3(x3+1x3)=1331000
x9+1x9+3(x3+1x3)=1331000
x9+1x9+3×110=1331000
(x3+1x3=110)
x9+1x9=1331000330=1330670
∴ Sum of digits = 1 + 3 + 3 + 0 + 6 + 7 + 0 = 20
Hence, the correct answer is option (3).

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebraic Identities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon