+0  
 
0
497
2
avatar

the product of two numbers is six times their sum. the sum of their squares is 325. what are the two numbers?

Guest Oct 13, 2014

Best Answer 

 #1
avatar+17745 
+5

I'm assuming that you want an exact answer, not a graphical approximation (which is a lost easier!):

x² + y²  =  325  ===>  x² + 2xy + y²  =  325 + 2xy  ===>  (x + y)²  =  325 + 2·6(x + y)

===>  (x + y)²  =  325 + 12(x + y)     ===>  (x + y)² - 12(x + y) - 325  =  0

Factor or use the quadratic formula:  [(x + y) - 25][(x + y ) + 13]  =  0

===>  x  =  25    or    x  =  -13

If x + y  =  25    ===>     y  =  25 - x

x² + y²  =  325   ===>   x² + (25 - x)²  =  325   ===>   x² + 625 - 50x + x²  =  325

===>   2x² - 50x + 300  =  0   ===>   x² - 25x + 150  =  0 

Factoring:  (x - 15)(x - 10)  =  0   ===>  x  =  15     or     x  =  10

===>  when x  =  10,  y  =  15; when x = 15, y = 10

Now, x = -13  gives you two more answers; in a similar solution as the above:  x  =  (-13 ± √481 ) / 2

When x = (-13 + √481 ) / 2, y = (-13 - √481 ) / 2  

and  when x = (-13 - √481 ) / 2, y = (-13 + √481 ) / 2

geno3141  Oct 13, 2014
 #1
avatar+17745 
+5
Best Answer

I'm assuming that you want an exact answer, not a graphical approximation (which is a lost easier!):

x² + y²  =  325  ===>  x² + 2xy + y²  =  325 + 2xy  ===>  (x + y)²  =  325 + 2·6(x + y)

===>  (x + y)²  =  325 + 12(x + y)     ===>  (x + y)² - 12(x + y) - 325  =  0

Factor or use the quadratic formula:  [(x + y) - 25][(x + y ) + 13]  =  0

===>  x  =  25    or    x  =  -13

If x + y  =  25    ===>     y  =  25 - x

x² + y²  =  325   ===>   x² + (25 - x)²  =  325   ===>   x² + 625 - 50x + x²  =  325

===>   2x² - 50x + 300  =  0   ===>   x² - 25x + 150  =  0 

Factoring:  (x - 15)(x - 10)  =  0   ===>  x  =  15     or     x  =  10

===>  when x  =  10,  y  =  15; when x = 15, y = 10

Now, x = -13  gives you two more answers; in a similar solution as the above:  x  =  (-13 ± √481 ) / 2

When x = (-13 + √481 ) / 2, y = (-13 - √481 ) / 2  

and  when x = (-13 - √481 ) / 2, y = (-13 + √481 ) / 2

geno3141  Oct 13, 2014
 #2
avatar+90023 
0

Very crafty the way you did that one geno !!!!

 

CPhill  Oct 14, 2014

15 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.