When you subtract one square number from another the answer is 35. What are the two square numbers?
+26387 When you subtract one square number from another the answer is 35. What are the two square numbers?
\(\begin{array}{rclrr} a^2 - b^2 &=& 35 \\ \underbrace{(a-b)}_{=5}\cdot \underbrace{(a+b)}_{=7} &=& 35 = 5\cdot 7 \\ \end{array}\)
\(\begin{array}{lrcl|r|r} & && & I. & II. \\ \hline & a-b &=& 5 & \\ & && & + & - \\ & a+b &=& 7 & \\ \hline \end{array} \)
\(\begin{array}{lrcl} I. \\ & 2a &=& 7+5 \\ & 2a &=& 12 \\ & a &=& 6 \\\\ II.\\ & 2b &=& 7-5\\ & 2b &=& 2 \\ & b &=& 1 \end{array}\)
\(\begin{array}{|rcll|} \hline 6^2 - 1^2 &=& 35 \\ \hline \end{array}\)
+26387 When you subtract one square number from another the answer is 35. What are the two square numbers?
\(\begin{array}{rclrr} a^2 - b^2 &=& 35 \\ \underbrace{(a-b)}_{=5}\cdot \underbrace{(a+b)}_{=7} &=& 35 = 5\cdot 7 \\ \end{array}\)
\(\begin{array}{lrcl|r|r} & && & I. & II. \\ \hline & a-b &=& 5 & \\ & && & + & - \\ & a+b &=& 7 & \\ \hline \end{array} \)
\(\begin{array}{lrcl} I. \\ & 2a &=& 7+5 \\ & 2a &=& 12 \\ & a &=& 6 \\\\ II.\\ & 2b &=& 7-5\\ & 2b &=& 2 \\ & b &=& 1 \end{array}\)
\(\begin{array}{|rcll|} \hline 6^2 - 1^2 &=& 35 \\ \hline \end{array}\)
