Question 970352

Step 1) Expand out the second equation using the distributive property or FOIL. 


Step 2) Use the first equation to simplify. 


Step 3) Isolate mn.


{{{ (2m-3n)^2=13 }}}


{{{ (2m-3n)(2m-3n)=13 }}} Using the idea {{{x^2 = x*x}}}


{{{ 2m(2m-3n)-3n(2m-3n)=13 }}} Distributive property


{{{ 4m^2 - 6mn - 6mn + 9n^2=13 }}} Distributive property


{{{ 4m^2 - 12mn + 9n^2=13 }}} Combine like terms


{{{ (4m^2 + 9n^2) - 12mn = 13 }}} Regrouping terms (associative property of addition)


{{{ 1 - 12mn = 13 }}} Replace {{{ 4m^2+9n^2 }}} with 1 (valid since {{{ 4m^2+9n^2=1 }}})


Now we solve for mn.


{{{ -12mn = 13-1 }}}


{{{ -12mn = 12 }}}


{{{ mn = 12/(-12) }}}


{{{ mn = -1 }}}