We want to find integer solutions to a'+b' =9c'. First, we divide both sides by c...

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We want to find integer solutions to a'+b' =9c'. First, we divide both sides by c³ and let x=a/c and y=b/c. What equation do we obtain? Note that we will be looking for rational solutions to this new equation. 2. There is an obvious solution to the equation in #1 having integer coordinates. Call this point P. Find the equation of the tangent line to the curve at P. Now find the other point where this line meets the curve. Note that reversing the coordinates still gives a solution. Call this point Q. 3. Find the equation of the line through points P and Q. Determine the third point R where this line meets the curve. 4. Use points and R to find integer solutions to our equation in #1. We want to find integer solutions to a'+b' =9c'. First, we divide both sides by c³ and let x=a/c and y=b/c. What equation do we obtain? Note that we will be looking for rational solutions to this new equation. 2. There is an obvious solution to the equation in #1 having integer coordinates. Call this point P. Find the equation of the tangent line to the curve at P. Now find the other point where this line meets the curve. Note that reversing the coordinates still gives a solution. Call this point Q. 3. Find the equation of the line through points P and Q. Determine the third point R where this line meets the curve. 4. Use points and R to find integer solutions to our equation in #1.

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To find rational solutions to the equation a b 9c we divide both sides by c and introduce new variab... View the full answer