What are the two square numbers?

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When you subtract one square number from another the answer is 35. What are the two square numbers?

Guest Nov 21, 2016

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When you subtract one square number from another the answer is 35. What are the two square numbers?

$\begin{array}{rclrr} a^2 - b^2 &=& 35 \\ \underbrace{(a-b)}_{=5}\cdot \underbrace{(a+b)}_{=7} &=& 35 = 5\cdot 7 \\ \end{array}$

$\begin{array}{lrcl|r|r} & && & I. & II. \\ \hline & a-b &=& 5 & \\ & && & + & - \\ & a+b &=& 7 & \\ \hline \end{array}$

$\begin{array}{lrcl} I. \\ & 2a &=& 7+5 \\ & 2a &=& 12 \\ & a &=& 6 \\\\ II.\\ & 2b &=& 7-5\\ & 2b &=& 2 \\ & b &=& 1 \end{array}$

$\begin{array}{|rcll|} \hline 6^2 - 1^2 &=& 35 \\ \hline \end{array}$

heureka Nov 21, 2016

heureka · Answer 1 · 2016-11-21T10:50:54

When you subtract one square number from another the answer is 35. What are the two square numbers?

$\begin{array}{rclrr} a^2 - b^2 &=& 35 \\ \underbrace{(a-b)}_{=5}\cdot \underbrace{(a+b)}_{=7} &=& 35 = 5\cdot 7 \\ \end{array}$

$\begin{array}{lrcl|r|r} & && & I. & II. \\ \hline & a-b &=& 5 & \\ & && & + & - \\ & a+b &=& 7 & \\ \hline \end{array}$

$\begin{array}{lrcl} I. \\ & 2a &=& 7+5 \\ & 2a &=& 12 \\ & a &=& 6 \\\\ II.\\ & 2b &=& 7-5\\ & 2b &=& 2 \\ & b &=& 1 \end{array}$

$\begin{array}{|rcll|} \hline 6^2 - 1^2 &=& 35 \\ \hline \end{array}$

Alan · Answer 2 · 2016-11-21T09:30:38

6^2 - 1^2 = 36 - 1 → 35

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