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) (Show Source): You can put this solution on YOUR website!
let a be the larger number.
let b be the smaller number.
formulas are:
(first equation)
(second equation)
use the first equation to solve for a in terms of b.
first equation is:
subtract from both sides of this equation to get:
square both sides of this equation to get:
substitute in second equation to get:
combine like terms to get:
subtract 25 from both sides of this equation to get:
divide both sides of this equation by (-10) to get:
square both sides of this equation to get:
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.
becomes becomes 3+2 = 5 confirming second equation is true.
answer is:
the numbers are 4 and 9.
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