Question

evaluate using suitable algebraic identity (x^5+1/2) (x^5-2)​

Answer 1

(x⁵ + ½)(x⁵ - 2)

= (x⁵)² + [½ + (-2)]x⁵ + (½)(-2)

... since (x + a)(x + b) = x² + (a + b)x + ab

= x¹⁰ + (½ - 2)x⁵ - (½)(2)

= x¹⁰ + (-3/2)x⁵ - (1)

= x¹⁰ - 3x⁵/2 - 1

Hence, (x⁵ + ½)(x⁵ - 2) = x¹⁰ - 3x⁵/2 - 1