Question

if x = √3+√2/√3-√2 then find : 1] x²+1/x² 2] x^4+1/x^4​

Answer 1

Answer:

98 and 9602

Step-by-step explanation:

x = (√3+√2)/(√3-√2)

x = (√3+√2)²/1

x = 5 + 2√6

So,

1/x = 5 - 2√6

Therefore,

x + 1/x = 10

(i) x + 1/x = 10

Squaring,

x² + 2 + 1/x² = 100

x² + 1/x² = 98

(ii) x² + 1/x² = 98

Squaring,

x⁴ + 2 + 1/x⁴ = 9604

x⁴ + 1/x⁴ = 9602