Question

I will mark you BRAINLIST ​

Answer 1

First, simplify the value of x:

(√3 + √2)/(√3 - √2) = (√3 + √2)/(√3 - √2) × (√3 + √2)/(√3 + √2)

= (3 + 2 + 2√6)/3 - 2

= 5 + 2√6

(i) x² + 1/x²

This can be written as:

(x + 1/x)² - 2

→ (5 + 2√6 + 1/(5 + 2√6))² - 2

→ (5 + 2√6 + 5 - 2√6)² - 2

→ 100 - 2

→ 98

(ii) x³ + 1/x³

This can be written as:

(x + 1/x)³ - 3(x + 1/x)

We found these values in the previous part:

→ 10³ - 3(10)

→ 1000 - 30

→ 970

The identities used:

• (a + b)² = a² + b² + 2ab
• (a + b)³ = a³ + b³ + 3ab(a + b)