Question

If a=2-root 5/2+root 5 and b=2+root 5 /2-root 5,find (a+b)^3​

Answer 1

Answer:

-5832

Step-by-step explanation:

$a = \frac{2 - \sqrt{5} }{2 + \sqrt{5} } \\ = \frac{2 - \sqrt{5} }{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} } \\ = \frac{(2 - \sqrt{5} ) {}^{2} }{ ({2}^{2}) - (\sqrt{5}) {}^{2} } \\ = 4 \sqrt{5 } - 9$

SIMILARLY-

$b = - 9 - 4 \sqrt{5}$

THUS-

$a + b = 4 \sqrt{5} - 9 - 9 - 4 \sqrt{5} = - 18 \\ = > (a + b) {}^{3} = ( - 18) {}^{3} = - 5832$

Answer 2

(a + b)³ = - 5832

Refer the attachment for complete answer ✔️