Question

If a = and b = find (a + b)3​

Answer 1

Step-by-step explanation:

a = (2-√5)/(2+√5)

(rationalising a)

= (2-√5)/(2+√5) × (2-√5)/(2-√5)

= {(2-√5)×(2-√5)}/{(2+√5)×(2-√5)}

= (2-√5)²/(2²-(√5)²

= (4+5-4√5)/(4-5)

= (9-4√5)/(-1)

= -9+4√5

b = (2+√5)/(2-√5)

(rationalising b)

= (2+√5)/(2-√5) × (2+√5)/(2+√5)

= {(2+√5)×(2+√5)}/{(2-√5)×(2+√5)}

= (2+√5)²/(2²-(√5)²

= (4+5+4√5)/(4-5)

= (9+4√5)/(-1)

= -9-4√5

(a+b)³

= (-9+4√5 + -9-4√5)³

= (-18)³

= -5832