SOLUTION: One number is one-third of another. The difference of their squares is ¾. Find the numbers.

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Question 674189: One number is one-third of another. The difference of their squares is ¾. Find the numbers.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=one number
Then (1/3)x or x/3=the other number
Sooooo we are told:
x^2-(x/3)^2=3/4
x^2-x^2/9=3/4
(8/9)x^2=3/4
x^2=(3/4)/(8/9) multiply numerator and denominator of rt side by 9/8 to get rid of complex fraction
x^2=(3/4)(9/8)/(8/9)(9/8)=27/32
x=+-sqrt(27/32)=+-sqrt((3*9)/(2*16))=3*sqrt(3)/4*sqrt(2)=(3/4)sqrt(3/2)
x/3=(1/4)*sqrt(3/2)
CK
((3/4)(sqrt(3/2))^2-((1/4)(sqrt(3/2))^2=3/4
(9/16)*(3/2)-(1/16)*(3/2)=3/4
(27/32)-(3/32)=3/4
24/32=3/4
3/4=3/4
Hope this helps----ptaylor