wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The sum of the squares of the digits of a two-digit number is 13. If we subtract 9 from that number, we get a number consisting of the same digits written in the reverse order. Find the number.

Open in App
Solution

Let the digits be x and y
The sum of square of the number is 13
x2+y2=13
Given that if 9 is subtracted from the number, it get reversed
(10x+y)9=10y+x
9x9y=9
xy=1
Now, (xy)2=x2+y22xy
1=132xy
2xy=12
xy=6y=6x
xy=1
x6x=1
x26=x
x2x6=0
x2+2x3x6=0
x(x+2)3(x+2)=0
(x+2)(x3)=0
(x+2)=0 and (x3)=0
x=2,3
Hence, the number is 32.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Playing with 2 - Digit and 3 - Digit Numbers
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon