a ) Using suitable identity solve this :-
b ) If , then find the value of
Answers
Answered by
32
Question no. 1 :
Using suitabIe identity soIve this :
200x⁴ - 675xy³
SoIution :
⇒ 200x⁴ - 675xy³
⇒ 25x(8x³ - 27y³)
⇒ 25x[(2x)³ - (3y)³]
⇒ 25x[(2x - 3y){(2x)² + 2x × 3y + (3y)²}]
⇒ 25x[(2x - 3y){4x² + 6xy + 9y²}] ············ (Required answer)
------------------------------------------------------
------------------------------------------------------
Question no. 2 :
If x⁴ + 1/x⁴ = 119 , then find the vaIue of x⁶ + 1/x⁶
SoIution :
⇔ x⁴ + 1/x⁴ = 119 ················· (i)
⇒ (x²)² + (1/x²)² = 119
⇒ (x² + 1/x²)² - 2 * x² * 1/x² = 119
⇒ (x² + 1/x²)² = 119 + 2
⇒ (x² + 1/x²)² = 121
⇒ x² + 1/x² = √121
⇒ x² + 1/x² = 11 ·············· (ii)
Now muItipIying (i) and (ii) :-
⇒ (x⁴ + 1/x⁴)(x² + 1/x²) = 119 * 11
⇒ x⁶ + (x⁴/x²) + (x²/x⁴) + 1/x⁶ = 1309
⇒ x⁶ + (x² + 1/x²) + 1/x⁶ = 1309
⇒ x⁶ + 1/x⁶ + 11 = 1309
⇒ x⁶ + 1/x⁶ = 1309 - 11
⇒ x⁶ + 1/x⁶ = 1298 ··························· (Required answer)
Similar questions
Math,
3 months ago
Computer Science,
3 months ago
Business Studies,
3 months ago
History,
7 months ago
Biology,
7 months ago
Math,
11 months ago
Geography,
11 months ago
Biology,
11 months ago