यदि \({\rm X} + \frac{1}{{\rm X}} = - 2\) है, तो x¹⁷ + x^-17 + x¹² + x^-12 का मान क्या है? (x < 0)

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 03 Dec 2022 Shift 2)

Answer 1

दिया गया है:

\({\rm X} + \frac{1}{{\rm X}} = - 2\)

गणना:

\({\rm X} + \frac{1}{{\rm X}} = - 2\)

x = - 1 के लिए, \({\rm X} + \frac{1}{{\rm X}} = - 2\)

इसलिए,

x17 + x-17 + x12 + x-12

⇒ x17 + \( \frac{1}{\rm x^{17}}\) + x12 + \( \frac{1}{\rm x^{12}}\)

⇒ - 1 - 1 + 1 + 1

⇒ - 2 + 2

⇒ 0

∴ अभीष्ट उत्तर 0 है।