If a – b = 3 and a2 + b2 = 149, find a + b.

Sure, let's solve this step by step:

Step 1: We know that (a - b)² = a² - 2ab + b². Given a - b = 3, we can square both sides to get (a - b)² = 9.

Step 2: Substitute a² + b² - 2ab = 9 (from step 1) into the equation a² + b² = 149. We get 149 - 2ab = 9.

Step 3: Solve for 2ab by subtracting 9 from 149, which gives 2ab = 140.

Step 4: Divide both sides by 2 to solve for ab, which gives ab = 70.

Step 5: We know that (a + b)² = a² + 2ab + b². Substitute a² + b² + 2*70 = (a + b)² into the equation a² + b² = 149. We get 149 + 140 = (a + b)².

Step 6: Solve for (a + b)² by adding 149 and 140, which gives (a + b)² = 289.

Step 7: Take the square root of both sides to solve for a + b. The square root of 289 is 17.

So, a + b = 17.