a = √5 + √4 হলে, a³ + 1/a³ এর মান কত?

a = √5 + √4
∴ 1/a = 1/(√5 + √4)
= (√5 - √4)/(√5 + √4)(√5 - √4)
= (√5 - √4)/(5 - 4)
= √5 - √4

∴ a + 1/a = √5 + √4 +√5 - √4 = 2√5

এখন, a³ + 1/a³
= (a + 1/a)³ - 3 × a × (1/a) × (a + 1/a)
= (2√5)³ - 3 × 2√5
= 8 × 5√5 - 6√5
= 40√5 - 6√5
= 34√5