Question

$\huge{\underline{\underline{\tt{\pink{Question}}}}}\:$

a ) Using suitable identity solve this :-
$200x^4\:-\:675xy^3$

b ) If $x^4\:+\:\frac{1}{x^4}\:=\:119$ , then find the value of $x^6\:+\:\frac{1}{x^6}$​

Answer 1

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)

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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)