14. If 𝑎 = √3−√2√3+√2 and 𝑏 = √3+√2√3−√2 then find the value of 𝑎2 + 𝑏2 − 3𝑎𝑏.

Sure, let's solve this step by step.

Step 1: Given 𝑎 = √3−√2/√3+√2 and 𝑏 = √3+√2/√3−√2

Step 2: Square both 𝑎 and 𝑏.

𝑎² = (√3−√2)²/(√3+√2)² = (3 - 2√6 + 2)/(3 + 2√6 + 2) = 1

𝑏² = (√3+√2)²/(√3−√2)² = (3 + 2√6 + 2)/(3 - 2√6 + 2) = 1

Step 3: Find the product of 𝑎 and 𝑏.

𝑎𝑏 = (√3−√2/√3+√2) * (√3+√2/√3−√2) = 1

Step 4: Substitute 𝑎², 𝑏² and 𝑎𝑏 into the expression 𝑎² + 𝑏² − 3𝑎𝑏.

𝑎² + 𝑏² − 3𝑎𝑏 = 1 + 1 - 3*1 = -1

So, the value of 𝑎² + 𝑏² − 3𝑎𝑏 is -1.