Question

answer in brief please ​

Answer 1

Qᴜᴇsᴛɪᴏɴ:-

If a = 1 - √2, find (a - 1/a)³

Fᴏʀᴍᴜʟᴀ Usᴇᴅ:-

• a² - b² = (a - b)(a + b)

Aɴsᴡᴇʀ:-

Finding 1/a :-

a = 1 - √2

➮1/a = 1/(1 - √2)

➮1/a = [1(1 + √2)] / [(1 - √2)(1 + √2)] [Rationalisation]

➮1/a = [(1 + √2)] / [(1)² - (√2)²] [By a² - b² formula]

➮1/a = (1 + √2) / (1 - 2)

➮1/a = (1 + √2) / (-1)

➮1/a = -(1 + √2)

➮1/a = -1 - √2

Finding a - 1/a :-

a - 1/a

➮1 - √2 - (-1 - √2)

➮1 - √2 + 1 + √2

➮a - 1/a = 2

Finding (a - 1/a)³ :-

(a - 1/a)³ = (2)³

➮(a - 1/a)³ = 8

Ans. = 8