Question 1032428
Let the numbers be {{{ a }}} and {{{ b }}}
(1) {{{ b - a = 3 }}}
(2) {{{ 1/a + 1/b = 7/10 }}}
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(1) {{{ b = a + 3 }}}
and
Multiply both sides of (2) by {{{ 10a*b }}}
(2) {{{ 10b + 10a = 7a*b }}}
(2) {{{ 7a*b - 10b = 10a }}}
(2) {{{ b*( 7a - 10 ) = 10a }}}
Substitute (1) into (2)
(2) {{{ ( a + 3 )*( 7a - 10 ) = 10a }}}
(2) {{{ 7a^2 + 21a - 10a - 30 = 10a }}}
(2) {{{ 7a^2 + a - 30 = 0 }}}
Use quadratic formula
{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = 7 }}}
{{{ b = 1 }}}
{{{ c = -30 }}}
{{{ x = (-1 +- sqrt( 1^2 - 4*7*(-30) )) / (2*7) }}} 
{{{ x = (-1 +- sqrt( 1 + 840 )) / 14 }}} 
{{{ x = (-1 +- sqrt( 841 )) / 14 }}} 
{{{ x = ( -1 + 29 ) / 14 }}}
{{{ x = 28/14 }}}
{{{ x = 2 }}}
So, {{{ a = 2 }}}
and
(1) {{{ b = a + 3 }}}
(1) {{{ b = 2 + 3 }}}
(1) {{{ b = 5 }}}
The numbers are 2 and 5
check:
(2) {{{ 1/a + 1/b = 7/10 }}}
(2) {{{ 1/2 + 1/5 = 7/10 }}}
(2) {{{ 5/10 + 2/10 = 7/10 }}}
(2) {{{ 7/10 = 7/10 }}}
OK