Wednesday

March 4, 2015

March 4, 2015

Posted by **LP** on Friday, January 4, 2013 at 7:23am.

The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.

- Math -
**Bosnian**, Friday, January 4, 2013 at 8:02ama = first number

b = second number

a - b = 3 Add b to both sides

a - b + b = 3 + b

a = b + 3

a ^ 2 + b ^ 2 = 89

( b + 3 ) ^ 2 + b ^ 2 = 89

b ^ 2 + 2 * b * 3 + 3 ^ 2 + b ^ 2 = 89

b ^ 2 + 6 b + 9 + b ^ 2 = 89

2 b ^ 2 + 6 b + 9 = 89 Divide both sides by 2

b ^ 2 + 3 b + 9 / 2 = 89 / 2 Subtract 9 / 2 to both sides

b ^ 2 + 3 b + 9 / 2 - 9 / 2 = 89 / 2 - 9 / 2

b ^ 2 + 3 b = 80 / 2

b ^ 2 + 3 b = 40 Add 9 / 4 to both sides

b ^ 2 + 3 b + 9 / 4 = 40 + 9 / 4

b ^ 2 + 3 b + 9 / 4 = 160 / 4 + 9 / 4

b ^ 2 + 3 b + 9 / 4 = 169 / 4

________________________________________

Remark :

b ^ 2 + 3 b + 9 / 4 = ( b + 3 / 2 ) ^ 2

________________________________________

( b + 3 / 2 ) ^ 2 = 169 / 4 take sqrt to both sides

b + 3 / 2 = 13 / 2 Subtract 3 / 2 to both sides

b + 3 / 2 - 3 / 2 = 13 / 2 - 3 / 2

b = 10 / 2 = 5

a = b + 3 = 5 + 3 = 8

Nuumbers are :

5 and 8

Proof :

8 - 5 = 3

8 ^ 2 + 5 ^ 2 = 64 + 25 = 89

**Answer this Question**

**Related Questions**

algebra word problem - the difference between 2 numbers is 24. find the numbers ...

finding numbers - The sum of two positive numbers is 20. Find the numbers if the...

Reiny! Reiny! Reiny! Answer Check and HW Help! - Translate to a system of ...

math - the lcm of two numbers is 30 the difference between the 2 numbers is 5 ...

math - The difference between two numbers is 36. The sum of these two numbers is...

math URGENT!!!! - i have a list of 5 different numbers. the sum of 2 of the ...

algebra - The sum of two numbers is 20. The difference of their squares is 120. ...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

math-word problems with quadratics - I have 5 questions... 1) The sum of two ...