SOLUTION: the sum of the the digits of a two-digit number is 10. The tens digit is 2 less than the square of the units digit. Find the number.

Question 527446: the sum of the the digits of a two-digit number is 10. The tens digit is 2 less than the square of the units digit. Find the number.
Answer by mathstutor494(120) (Show Source): You can put this solution on YOUR website!
Let unit digit be y and tens digit be x
Therefore the number is 10x+y
Further, given that sum of the the digits of a two-digit number is 10
So x+y =10 ...............................................(1)
Also given that the tens digit is 2 less than the square of the units digit
So x= y^2-2...............................................(2)
Substituting value of x from eq 1 in eq 2 results in
10-y = y^2 -2
Rearranging above terms of the eq results in
y^2+y-12=0
y^2+4y-3y-12=0
y(y+4)-3(y+4)=0
(Y-3)(Y+4)=0
So y = 3 or -4
As the digit can not be negative, therefore y=3
Hence x=7 (from eq 1)
Therefore the number is = 7*10+3
Ans = 73

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