SOLUTION: x/y = a/b = 2/3 y² - b² = 27 x² - a² = ?

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Question 1210347: x/y = a/b = 2/3
y² - b² = 27
x² - a² = ?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%2Fy = a%2Fb = 2%2F3
y%5E2 - b%5E2 = 27
x%5E2 - a%5E2 = ?
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The solution is in couple of lines. 


From the given part in the first line we have

    x = %282%2F3%29y,  a = %282%2F3%29%2Ab.


Hence,

      x%5E2-a%5E2 = %284%2F9%29%2Ay%5E2+-+%284%2F9%29%2Ab%5E2 = %284%2F9%29%2A%28y%5E2-b%5E2%29 = 

           substitute here  y%5E2+-+b%5E2 = 27  from the second given line

    = %284%2F9%29%2A27 = 4*3 = 12.


ANSWER.  Under given conditions,  x%5E2+-+a%5E2 = 12.

Solved.