যদি (x² - ) = 4 এবং x > 1 হয়, তাহলে (x³ - ) এর মান কত?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 3)

Answer 1

প্রদত্ত:

(x2 - ) = 4 = (x + )(x - ) ...(1)

উভয় পক্ষকে বর্গ করলে

⇒ (x² - )² = 16 x 6

⇒ x4 + - 2 = 96

⇒ x4 + = 98

⇒ x4 + + 2 = 98 + 2

⇒ (x2 + )² = 100

⇒ x2 + = 10

⇒ x2 + + 2 = 10 + 2

⇒ (x + )² = 12

⇒ x + = √12 = 2√3 ...(2)

সুতরাং

⇒ x - = 2√2 [সমীকরণ (1) কে (2) দিয়ে ভাগ করে]

এবং

(x - )3 = (x3 - ) - 3 (x - )

⇒ (2√2)³ = x3 - - 3(2√2)

⇒ 16√2 + 6√2 = x3 -

⇒ x3 - = 22√2