SOLUTION: a number is one less than twice another number,and the difference between their squares is 85. find the numbers
Algebra.Com
Question 1109206: a number is one less than twice another number,and the difference between their squares is 85. find the numbers
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a number is one less than twice another number,
a = 2b - 1
and the difference between their squares is 85.
a^2 - b^2 = 85
replace a with (2b-1)
(2b-1)^2 - b^2 = 85
FOIL (2b-1)(2b-1)
4b^2 - 2b - 2b + 1 - b^2 = 85
Combine to form a quadratic equation on the left
3b^2 - 4b + 1 - 85 = 0
3b^2 - 4b - 84 = 0
you can use the quadratic formula; a=3; b=-4; c=-84, but this will factor
(3b+14)(b-6) = 0
The positive integer solution
b = 6
Find a
a = 2(6) - 1
a = 11
:
find the numbers 11, 6
:
:
Check:
11^2 - 6^2 =
121 - 36 - 85
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The statement of the problem implies that the numbers are whole numbers. So solving the problem requires less work if you look for numbers for which the difference of the squares is 85 and find such a pair with one of the numbers being 1 less than twice the other.
There are two possibilities in whole numbers:
; --> (a,b) = (43,42) no....
; --> (a,b) = (11,6) YES!!!
RELATED QUESTIONS
One number is one less than twice another, and the difference between their squares is... (answered by macston)
One number is one less than twice another, and the difference between squares is 16, find (answered by Cromlix,MathTherapy)
One number is three less than twice another. The sum of their squares is 74. Find the... (answered by stanbon)
One number is 5 more than another. The difference between their squares is 95. What are... (answered by ankor@dixie-net.com)
One number is 5 more than another. The difference between their squares is 165. What are... (answered by ewatrrr)
one number is 3 more than another. the difference between their squares is 75. what are... (answered by TimothyLamb)
One number is 3 more than another. The difference between their squares is 57. What are... (answered by TimothyLamb)
One number is 6 more than another. the difference between their squares is 84. what are... (answered by TimothyLamb)
one number is 6 more than another the difference between their squares is 192 what are... (answered by amarjeeth123)