SOLUTION: 36.) Show a complete solution to the problem. Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers.

Algebra ->  Test  -> Lessons -> SOLUTION: 36.) Show a complete solution to the problem. Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers.      Log On


   

Question 165236: 36.) Show a complete solution to the problem.
Two positive numbers differ by 11, and their square roots differ by 1. Find the numbers.
Found 2 solutions by edjones, josmiceli:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
a) x-y=11
b) sqrt(x)-sqrt(y)=1
.
a)x=y+11
b)
sqrt(x)=sqrt(y)+1
x=y+1+2sqrt(y) square each side.
y+11=y+1+2sqrt(y) substitute y+11 for x
10=2sqrt(y)
5=sqrt(y)
y=25 square each side.
x=36
.
Ed

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the numbers a and b
(1) b+-+a+=+11
(2) sqrt%28b%29+-+sqrt%28a%29+=+1
Let c%5E2+=+a
Let d%5E2+=+b
------------------
d%5E2+-+c%5E2+=+11
%28d+-+c%29%28d+%2B+c%29+=+11
d+-+c+=+1
1%2A%28d+%2B+c%29+=+11
d+%2B+c+=+11
Add these equations
2d+=+12
d+=+6
d+-+c+=+1
6+-+c+=+1
c+=+5
--------------
c%5E2+=+a
5%5E2+=+a
a+=+25
d%5E2+=+b
6%5E2+=+b
b+=+36
The numbers are 25 and 36
check:
The numbers differ by 11 and
their square roots differ by 1