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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?
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 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
so from eqn 1 y=9-5=4
so the no is 54 ans