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

Question

Accepted Answer

Given x = 7 - 4√3.

Step 1: Calculate x².
x² = (7 - 4√3)² = 7² - 2*7*4√3 + (4√3)²
= 49 - 56√3 + 16*3
= 49 - 56√3 + 48
= 97 - 56√3

Step 2: Calculate 1/x.
Since x = 7 - 4√3, its conjugate is 7 + 4√3.

1/x = 1/(7 - 4√3) = (7 + 4√3)/[(7)² - (4√3)²]
= (7 + 4√3)/(49 - 16*3)
= (7 + 4√3)/(49 - 48)
= 7 + 4√3

Step 3: Calculate 1/x² = (1/x)² = (7 + 4√3)²
= 7² + 2*7*4√3 + (4√3)²
= 49 + 56√3 + 48
= 97 + 56√3

Step 4: Calculate x² + 1/x²
= (97 - 56√3) + (97 + 56√3)
= 97 + 97 + (-56√3 + 56√3)
= 194 + 0
= 194

Therefore, the value of (x² + 1/x²) is 194.

Answer

Answer

Answer