ᴩʟᴇᴀꜱᴇ ᴄᴀɴ ꜱᴏᴍᴇᴏɴᴇ ꜱᴏʟᴠᴇ ᴛʜɪꜱ qᴜᴇꜱᴛɪᴏɴ
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ᴩʟᴇᴀꜱᴇ ᴄᴀɴ ꜱᴏᴍᴇᴏɴᴇ ꜱᴏʟᴠᴇ ᴛʜɪꜱ qᴜᴇꜱᴛɪᴏɴ
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Qᴜᴇsᴛɪᴏɴ :- if a ≠ 0 and (a - 1/a) = 3 ; find :-
Sᴏʟᴜᴛɪᴏɴ :-
→ (a - 1/a) = 3
Squaring Both sides we get,
→ (a - 1/a)² = 3²
Now using (a - b)² = a² + b² - 2ab in LHS,
→ a² + 1/a² - 2 * a * 1/a = 9
→ (a² + 1/a²) - 2 = 9
→ (a² + 1/a²) = 9 + 2
→ (a² + 1/a²) = 11 (Ans.)
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Again,
→ → (a - 1/a) = 3
Cubing Both sides we get,
→ (a - 1/a)³ = 3³
Now using (a - b)³ = a³ - b³ - 3ab(a - b) in LHS,
→ a³ - 1/a³ - 3 * a * 1/a(a - 1/a) = 27
→ a³ - 1/a³ - 3 * (a - 1/a) = 27
Putting value of (a - 1/a) = 3 Now,
→ a³ - 1/a³ - 3 * 3 = 27
→ a³ - 1/a³ - 9 = 27
→ (a³ - 1/a³) = 27 + 9
→ (a³ - 1/a³) = 36 (Ans.)
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