Question

The sum of digits of a two digit number is 13. If sum of their squares is 89, find the

number.

Answer 1

Let the tens place digit be x and the units place digits be y

so by the condition given in the question
x+y=13. ----1

x^2+y^2=89

by squaring both the sides of equation 1 we get

x^2+2xy+y^2=169

89+2xy=169

2xy=169-89

xy=40

so

(x-y)^2=x^2-2xy +y^2

=89-80

=9

(x-y)^2=9

by taking square root of both the sides we get

x-y=3. ---3

by adding equation 1 and 3 we get

2x=16

x=8

y=5

so the number is 85