# Let x = (√13+√11)/(√13 – √11 and y=1, then the Value of 3x²-5xy+3y² is :

**Answer is (4)**: 1717

**Explanation:-**

x = (√13+√11)/(√13 – √11)

= (√13 + √11) (√13 + √11)/(√13 – √11) (√13 + √11)

= (√13 + √11)²/(√13)² – (√11)²

= {(√13)² + (√11)² + 2√13 x √11}/13 – 11

= (13 + 11 + 2 √13 √11)/2

= (24 + 2 √13 √11)/2

= 2 (12 + √13 √11)/2

x = 12 + √13 √11 and y = 1

Then, the value of 3x² -5 xy + 3 y²

Put the value of x = 12 + √13 √11 and y = 1

Then, 3 ( 12 + √13 √11)² – 5 (12 + √13 √11) (1) + 3 (1)²

= 3 (12)² + (√13 √11)² + 2 x 12 x √13 √11 – 60 + 5√13 √11 + 3

= 3 x 144 + 13 x 11 + 24√13 √11 – 60 + 5√13 √11 + 3

= 432 + 143 – 60 +3 + 24√13 √11 + 5√13 √11

= 518 + 29√13 √11

= 518 + 29 x 3.6 x 3.31

= 518 +