Question

The sum of the digits of a two digit number is 14. The tens digit is the square of a number which is 2 less than the units digit Find the two-digit number,​

Answer 1

Answer:

The sum of the digits of a two-digit number is 14.

t + u = 14

or

t = (14-u); use this form for substitution

:

The tens digit is the square of a number which is 2 less than the units digit.

t = (u-2)^2

FOIL (u-2)(u-2)

t = u^2 - 4u + 4

Replace t with (14-u)

14 - u = u^2 - 4u + 4

0 = u^2 - 4u + u + 4 - 14

A quadratic equation

u^2 - 3u - 10 = 0

Factors to

(u-5)(u+2) = 0

The positive solution is what we want here

u = 5

then

t = 14 - 5

t = 9

:

Find the two-digit number. 95

:

;

we can confirm this, in the 2nd statement

"The tens digit is the square of a number which is 2 less than the units digit."

9 = (5-2)^2

9 = 3^2