Question

if a=3+2√2 find the value of a²-1​

Answer 1

Given: a = (3 + 2√2)

To Find: Value of (a² - 1).

We know, (a² - b²) = (a + b)(a - b)

also, (x + a)(x + b) = x² + (a + b)x + ab

∴ a² - 1 = [(3 + 2√2) + 1] • [(3 + 2√2) - 1]

⟹ a² - 1 = (3 + 2√2 + 1) • (3 + 2√2 - 1)

⟹ a² - 1 = (2√2 + 4) • (2√2 + 2)

⟹ a² - 1 = (2√2)² + (4 + 2)2√2 + (2)(4)

[∵ (x + a)(x + b) = x² + (a + b)x + ab]

⟹ a² - 1 = 8 + (6)2√2 + 8

⟹ a² - 1 = 16 + 12√2

∴ a² - 1 = 16 + 12√2