Question

chapter=Theory of quadratic equations

QUESTION=The sum of the square of two digits of a positive integral number is 65 and the number is 9 times the sum of its digits.Find the number.

Answer 1

x ^ 2 + y ^ 2 = 65 ........eq 1
9(x + y ) = 10x + y
9y + 9 x = 10x + y
8 y = x
put the value of x in eq 1
( 8y) ^2 + y ^ 2 = 65
64 y ^2 + y ^2 = 65
65 y ^ 2 = 65
y^ 2 = 1
y = 1,-1
neglecting = -1
and by keeping the value of y in eq 1 we get x = 8
so the number is 81