Question

If x = 3 and y = -1, find the values of each of the following using in identity: 

(i) (9y² – 4x²)(81y⁴ + 36x²y² + 16x⁴) 

(ii) \((\frac{3}{x} - \frac{x}{3})\) \((\frac{x^2}{9} + \frac{9}{x^2} + 1)\)

(iii) \((\frac{x}{7} + \frac{y}{3})\) \((\frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21})\)

(iv) \((\frac{x}{4} - \frac{y}{3})\) \((\frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9})\)

(v) \((\frac{5}{x} + 5x)\) \((\frac{25}{x^2} - 25 + 25x^2)\)

Answer 1

If x = 3 and y = -1

(i) (9y² – 4x²)(81y⁴ + 36x²y² + 16x⁴) 

= (9y² – 4x²) [(9y²)² + 9y² x 4x² + (4x²)²] 

= (9y²)³ – (4x²)³ 

= 729 y⁶ – 64 x⁶ 

= 729 x (-1)⁶ - 64 x (3)⁶

= 729 x 1 - 64 x 729

= 729 – 46656 

= – 45927

(ii)  \((\frac{3}{x} - \frac{x}{3})\) \((\frac{x^2}{9} + \frac{9}{x^2} + 1)\)

(iii)  \((\frac{x}{7} + \frac{y}{3})\) \((\frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21})\)

(iv)  \((\frac{x}{4} - \frac{y}{3})\) \((\frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9})\)

(v)  \((\frac{5}{x} + 5x)\) \((\frac{25}{x^2} - 25 + 25x^2)\)