Question

If a=√5+4√14 and b=√5-4√14 then find a^3+ b^3​

Answer 1

Step-by-step explanation:

a+b = √5+4√14+√5-4√14=2√5.

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} + {b}^{2} - ab) = >$

ab=(√5+4√14)(√5-4√14)=5-224 = -219

(a+b)=2√5 square on both sides we get

${(a + b)}^{2} = 20$

Hence

${a}^3 + {b}^{3} = 2 \sqrt{5} ( {(a + b)}^{2} - 3ab) =$

$2 \sqrt{5}(20 + 657) = 1354 \sqrt{5}$

Hope it helps you.