Question

Find value of (2+√5)^5+(2-√5)^5

Answer 1

Step-by-step explanation:

(2+√5)^5 + (2-√5)^5

(2+√5)²((2+√5)³ + (2-√5)²(2-√5)³

=(4+5+4√5)(8+5√5+3*4√5+3*2*5) + (4+5-4√5)(8-5√5-3*4*√5+3*2*5)

= (9+4√5)(8+5√5+12√5+30) + (9-4√5)(8-5√5-12√5+30)

=(9+4√5)(38+17√5) + (9-4√5)(38-17√5)

= (342+153√5+152√5+340) + (342-153√5-152√5+340)

= 2(342+340) = 2×682 = 1364