```Question 257190
let a be the larger number.
let b be the smaller number.

formulas are:

{{{sqrt(a) + sqrt(b) = 5}}} (first equation)

{{{a-b = 5}}} (second equation)

use the first equation to solve for a in terms of b.

first equation is:

{{{sqrt(a) + sqrt(b) = 5}}}

subtract {{{sqrt(b)}}} from both sides of this equation to get:

{{{sqrt(a) = 5 - sqrt(b)}}}

square both sides of this equation to get:

{{{a = 25 - 10*sqrt(b) + b}}}

substitute in second equation to get:

{{{25 - 10*sqrt(b) + b - b = 5}}}

combine like terms to get:

{{{25 - 10*sqrt(b) = 5}}}

subtract 25 from both sides of this equation to get:

{{{-10*sqrt(b) = 5-25 = -20}}}

divide both sides of this equation by (-10) to get:

{{{sqrt(b) = 2}}}

square both sides of this equation to get:

{{{b = 4}}}

if b = 4, than a-b = 5 becomes a-4 = 5 becomes a = 9.

you have:

a = 9
b = 4

a-b = 5 becomes 9-4 = 5 confirming second equation is true.

{{{sqrt(a) + sqrt(b) = 5}}} becomes {{{sqrt(9) + sqrt(4) = 5}}} becomes 3+2 = 5 confirming second equation is true.

the numbers are 4 and 9.

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