Question
If x4 + 1/x4=34 then what is the value of x3 – (1/x3)?
यदि x⁴ + 1/x⁴=34, तो (x³ - 1/x³) का मान क्या है?
A.
B.
C.
D.
Answer D.
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D.x⁴ + 1/x⁴=34 add 2 x² × 1/x² both side- x⁴ + 1/x⁴ + 2x² × 1/x² = 34 + 2x² × 1/x² (x² + 1/x²)² = 34 + 2 =(x² + 1/x²)² = 36 = (x² + 1/x²) = √36 = x² + 1/x² = 6 Again, subtract 2x × 1/x from both sides, x² + 1/x² - 2x × 1/x = 6 - 2x × 1/x =(x - 1/x)² = 6 - 2 =(x - 1/x)² = 4 = x - 1/x = √4 =x - 1/x = 2 (x - 1/x)^3=x³ - 1/x³ - 3 x * 1/x (x - 1/x) (2)^3=x³ - 1/x³ - 3 *(2) 8+6=x³ - 1/x³ x³ - 1/x³ =14 So the correct answer is option D.
D.x⁴ + 1/x⁴=34 2 x² × 1/x² को दोनों तरफ जोड़ने पर - x⁴ + 1/x⁴ + 2x² × 1/x² = 34 + 2x² × 1/x² (x² + 1/x²)² = 34 + 2 =(x² + 1/x²)² = 36 = (x² + 1/x²) = √36 = x² + 1/x² = 6 दोबारा 2x × 1/x को दोनों ओर घटाने पर x² + 1/x² - 2x × 1/x = 6 - 2x × 1/x =(x - 1/x)² = 6 - 2 =(x - 1/x)² = 4 = x - 1/x = √4 =x - 1/x = 2 (x - 1/x)^3=x³ - 1/x³ - 3 x * 1/x (x - 1/x) (2)^3=x³ - 1/x³ - 3 *(2) 8+6=x³ - 1/x³ x³ - 1/x³ =14 इसलिए सही उत्तर विकल्प D है।
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