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?

Answer 1

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Answer 2

Answer: 32

Step-by-step explanation: 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

9x−9y=9

x−y=1

Now, (x−y)2=x2+y2−2xy

⇒1=13−2xy

⇒2xy=12

⇒xy=6⇒y=x6​

⇒x−y=1

⇒x−x6​=1

⇒x2−6=x

⇒x2−x−6=0

⇒x2+2x−3x−6=0

⇒x(x+2)−3(x+2)=0

⇒(x+2)(x−3)=0

⇒(x+2)=0 and (x−3)=0

⇒x=2,3

Hence, the number is 32.