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If one number is $80\%$ of the other and $4$ times the sum of their squares is $656$, then What are the numbers?

My answer is -

let the two numbers be x and y.

$x = \frac 45 y$

$4(x^2 + y^2) = 656$

$\implies x^2 + y^2 = 164$

Now substitute $x =\frac 45 y$:

\begin{align} &\implies \frac{16}{25}y^2 + y^2 = 164\\ &\implies \frac{41}{25}y^2 = 164 \\ &\implies y^2 = 100 \end{align} therefore $y$ can be $10$ or $-10$.

and $x$ can be the $8$ or $-8$.

However, the answer given is $8$, and $10$. My doubt is the answer should be $8,10$ and $-8$,$-10$. Am I correct here?

Claude Leibovici
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dexterous
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    If no other condition is required on solutions, then both ${8,10}$ and ${-8,-10}$ are good. – Milly Oct 30 '14 at 03:32
  • Both are correct solutions but in real life situations, the negative solutions may be meaningless. – Jack Oct 30 '14 at 03:39
  • They both work. Perhaps there were more conditions? – Akiva Weinberger Oct 30 '14 at 03:43
  • No, this was the entire question. Also, If you see, I have asked the question on the percentages can be positive or negative in maths stack exchange. I got the answer as - percentages can be positive as well as negative. Another question, why I am down voted. – dexterous Oct 30 '14 at 06:58

1 Answers1

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Yes, if there are no other conditions, {8,10} and {-8,-10} are both valid answers. As for percentages being negative, a percent symbol just means divide by 100. So -125.658% is valid and so is 3^(1/2)%

ghosts_in_the_code
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