If 𝑎 + 𝑏 = 8 and 𝑎𝑏 = 14 , find(1) 𝑎2 + 𝑏2(2) 𝑎2 + 𝑎𝑏 + 𝑏2(3) (𝑎 − 𝑏)

Sure, let's solve these step by step:

(1) To find 𝑎² + 𝑏², we can use the formula (𝑎 + 𝑏)² - 2𝑎𝑏. We know that 𝑎 + 𝑏 = 8 and 𝑎𝑏 = 14. So, (𝑎 + 𝑏)² - 2𝑎𝑏 = 8² - 2*14 = 64 - 28 = 36.

(2) To find 𝑎² + 𝑎𝑏 + 𝑏², we can use the formula (𝑎 + 𝑏)² - 𝑎𝑏. We know that 𝑎 + 𝑏 = 8 and 𝑎𝑏 = 14. So, (𝑎 + 𝑏)² - 𝑎𝑏 = 8² - 14 = 64 - 14 = 50.

(3) To find (𝑎 - 𝑏), we can use the formula √[(𝑎 + 𝑏)² - 4𝑎𝑏]. We know that 𝑎 + 𝑏 = 8 and 𝑎𝑏 = 14. So, √[(𝑎 + 𝑏)² - 4𝑎𝑏] = √[8² - 4*14] = √[64 - 56] = √8.

Please note that the square root of 8 is a complex number, so (𝑎 - 𝑏) could be either √8 or -√8.