+789 Fill in the blanks with positive integers:
(3 + sqrt(5))^2*(2 - sqrt(5))^7 = ___ + ___ *sqrt(5)
+410 (3+√5)2∗(2−√5)7
Simplify the left side first:
(3+√5)2=14+6√5
Split some terms apart to find the right side.
(2−√5)2=9−4√5
(2−√5)4=(9−4√5)2=161−72√5
(2−√5)7=(2−√5)4∗(2−√5)2∗(2−√5).
=(161−72√5)(9−4√5)(2−√5)=12238−5473√5
With a little help from calculators, this is
(14+6√5)∗(12238−5473√5)=7142−3194√5.
+410 (3+√5)2∗(2−√5)7
Simplify the left side first:
(3+√5)2=14+6√5
Split some terms apart to find the right side.
(2−√5)2=9−4√5
(2−√5)4=(9−4√5)2=161−72√5
(2−√5)7=(2−√5)4∗(2−√5)2∗(2−√5).
=(161−72√5)(9−4√5)(2−√5)=12238−5473√5
With a little help from calculators, this is
(14+6√5)∗(12238−5473√5)=7142−3194√5.
