Given that a - b = 3 and ab=5, find, without the use of a calculator,
the value of a +b?

√29

Step-by-step explanation:

We are here given that ,

Now square the first equation ,

⇒ a - b = 3

⇒ ( a - b)² = 3²

⇒ a² + b² - 2ab = 9

⇒ a² + b² - 2(5) = 9

⇒ a² + b² -10 = 9

⇒ a² + b² = 9 + 10

⇒ a² + b² = 19

⇒ a² + b² + 2ab = 19 + 2(5)

⇒ (a + b)² = 19 + 10

⇒ ( a + b)² = 29

⇒ a + b = √29 .