SOLUTION: The sum of the square roots of two numbers is 5. The two numbers differ by 5. What are the numbers?

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Question 257190: The sum of the square roots of two numbers is 5. The two numbers differ by 5.
What are the numbers?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let a be the larger number.
let b be the smaller number.

formulas are:

sqrt%28a%29+%2B+sqrt%28b%29+=+5 (first equation)

a-b+=+5 (second equation)

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

first equation is:

sqrt%28a%29+%2B+sqrt%28b%29+=+5

subtract sqrt%28b%29 from both sides of this equation to get:

sqrt%28a%29+=+5+-+sqrt%28b%29

square both sides of this equation to get:

a+=+25+-+10%2Asqrt%28b%29+%2B+b

substitute in second equation to get:

25+-+10%2Asqrt%28b%29+%2B+b+-+b+=+5

combine like terms to get:

25+-+10%2Asqrt%28b%29+=+5

subtract 25 from both sides of this equation to get:

-10%2Asqrt%28b%29+=+5-25+=+-20

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

sqrt%28b%29+=+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%28a%29+%2B+sqrt%28b%29+=+5 becomes sqrt%289%29+%2B+sqrt%284%29+=+5 becomes 3+2 = 5 confirming second equation is true.

answer is:

the numbers are 4 and 9.