Question 165236
Call the numbers {{{a}}} and {{{b}}}
(1) {{{b - a = 11}}}
(2) {{{sqrt(b) - sqrt(a) = 1}}}
Let {{{c^2 = a}}}
Let {{{d^2 = b}}}
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{{{d^2 - c^2 = 11}}}
{{{(d - c)(d + c) = 11}}}
{{{d - c = 1}}}
{{{1*(d + c) = 11}}}
{{{d + c = 11}}}
Add these equations
{{{2d = 12}}}
{{{d = 6}}}
{{{d - c = 1}}}
{{{6 - c = 1}}}
{{{c = 5}}}
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{{{c^2 = a}}}
{{{5^2 = a}}}
{{{a = 25}}}
{{{d^2 = b}}}
{{{6^2 = b}}}
{{{b = 36}}}
The numbers are 25 and 36
check:
The numbers differ by 11 and
their square roots differ by 1