Question 136740
Try this!
Let T = the ten's digit and U = the unit's digit.
Then:
{{{T^2+U^2 = 20}}} and...
{{{T = U+2}}} Substitute this into the above equation:
{{{(U+2)^2+U^2 = 20}}} Simplify:
{{{U^2+4U+4+U^2 = 20}}}
{{{2U^2+4U+4 = 20}}} Subtract 20 from both sides.
{{{2U^2+4U-16 = 0}}} Factor out a 2.
{{{2(U^2+2U-8) = 0}}} Apply the zero products rule.
{{{U^2+2U-8 = 0}}} Factor.
{{{(U+4)(U-2) = 0}}} so...
{{{U+4 = 0}}} or {{{U-2 = 0}}}, then...
{{{U = -4}}} or {{{U = 2}}} Discard the negative solution.
{{{U = 2}}} This is the unit's digit.
{{{T = U+2}}}
{{{T = 2+2}}}
{{{T = 4}}} This is the ten's digit.
The number (TU) is 42.