Question 1146571
t = the tens digit
u = the units
:
Write an equation for each statement
:
the tens digits of a certain number is 7 less than the units digit.
t = u - 7
the sum of the squares of the two digits is 85.
t^2 + u^2 = 85
replace t with (u-7)
(u-7)^2 + u^2 = 85
FOIL(u-7)(u-7)
u^2 - 14u + 49 + u^2 - 85 = 0
2u^2 - 14u - 36 = 0
simplify divide 2
u^2 - 7u - 18 = 0
Factors to
(u-9)(u+2) = 0
the positive solutin
u = 9
then
t = 9 - 7
t = 2
find the number.with justification
Number is 29
:
:
Check: 2^2 + 9^2 = 81 + 4 = 85