Question

If x= (7+4√3), then the value of x²+(1/x²)​

Answer 1

Answer:

194

Step-by-step explanation:

x = 7 + 4√3

1/x = 1/(7 + 4√3)

on rationalizing :-

1/x = (1 × 7 - 4√3) / ((7 + 4√3) × ( 7 - 4√3))

= (7 - 4√3) / (49 - 48)

= (7 - 4√3) / 1

1/x = 7 - 4√3

x² + 1/x²

= (7 + 4√3)² + (7 - 4√3)²

= [7² + (4√3)² + 2×7×4√3] + [7² + (4√3)² - 2×7×4√3]

= 49 + 48 + 49 + 48 +  2×7×4√3 -  2×7×4√3

= 194 (Ans