Question:
If x + 1/x = 2, then find the value of (x^4 + 4/x^4)(x^3 – 4/x^3).
यदि x + 1/x = 2 है, तो (x^4 + 4/x^4)(x^3 – 4/x^3) का मान ज्ञात कीजिए।
Options:
- a) −10
- b) 10
- c) −15
- d) 15
- a) −10
- b) 10
- c) −15
- d) 15
correct answer : c)
Explanation:
Given x + 1/x = 2. This equation is satisfied only when x = 1. Substituting x = 1 in the expression: (1^4 + 4/1^4)(1^3 – 4/1^3) = (1 + 4)(1 – 4) = 5 * (-3) = -15.
दिया गया है x + 1/x = 2। यह समीकरण केवल तभी संतुष्ट होता है जब x = 1 हो। व्यंजक में x = 1 रखने पर: (1⁴ + 4/1⁴)(1³ – 4/1³) = (1 + 4)(1 – 4) = 5 * (-3) = -15।