SOLUTION: The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product

Question 634389: The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. What is the number?
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. What is the number?

ans:
let the the digit at tenths place=x & at ones place=y
as per question x+y=9 -eqn 1
& x2-xy+y2=21------eqn 2
from eqn 2 (x+y)2-3xy=21
or 3xy=(x+y)2-21=81-21=60
or xy=20 -----eqn 3
now (x-y)=sq rt[(x+y)2-4xy]=sq rt(81-80)=1--eqn 4
adding eqn 1 &eqn 4
2x=10
or x=5
so from eqn 1 y=9-5=4
so the no is 54 ans

RELATED QUESTIONS
The sum of both digits, of either of two two-digit numbers, in whatever order the digits... (answered by Nate)

The sum of both digits, of either of two two-digit numbers, in whatever order the digits... (answered by ankor@dixie-net.com)

The sum of both digits, of either of two two-digit numbers, in whatever order the digits... (answered by scott8148)

the sum of both digits of either of two two-digit numbers, in whatever order the digits... (answered by ankor@dixie-net.com)

The sum of both digits, of either of two two-digit numbers, in whatever order the digits... (answered by Edwin McCravy)

THE SUM OF BOTH DIGITS, OF EITHER OF TWO TWO-DIGET NUMBERS, IN WHATEVER ORDER THE DIGETS... (answered by edjones)

2. The sum of both digits, of either of two two-digit numbers, in whatever order the... (answered by ptaylor)

In a 4 digit number, the first two digits are both 2. The sum of the ones and tens digits (answered by solver91311)

The sum of digits of a two digit numbers is 9 and if 9 is added to the number the digits (answered by ikleyn)