anonymous
  • anonymous
the sum of the inverse of the positive intger x and the inverse of the whole number y is (sgrt 4913^(1/3))/60. if the product of the 2 numbers is 60, find the sum of their squares
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1378335279659:dw| here is the number again
anonymous
  • anonymous
anybody?
blockcolder
  • blockcolder
Which inverse are we talking about, the negative or the reciprocal?

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blockcolder
  • blockcolder
I'll just assume that inverse=reciprocal. The first statement is saying that \[\frac{1}{x}+\frac{1}{y}=\frac{\sqrt[n]{4913}}{60}\] but for the purpose of generality, I'll let the RHS be equal to k, that is, \[\frac{1}{x}+\frac{1}{y}=k\] where k can be any positive number.
blockcolder
  • blockcolder
In a similar way, the second statement is saying that \(xy=60\) but again, to cover the general case, we let \(xy=m\), where m is a positive number. Then we are tasked to look for the value of \(x^2+y^2\).
blockcolder
  • blockcolder
You can see in our first equation that \[\frac{x+y}{xy}=k\Rightarrow x+y=kxy\Rightarrow x+y=km.\] If we square the last equation, you get \[x^2+2xy+y^2=(km)^2 \Rightarrow x^2+y^2=(km)^2-2m\] then plug \(k=\frac{\sqrt[3]{4913}}{60}\) and \(m=60\).
anonymous
  • anonymous
thanks

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