No.
22
-4
The lengths of the sides of the triangle are: 2*sq rt of 10, 5*sq rt of 2 and sq rt of 10 The 3 sides added together equals the perimeter which works out as 3* sq rt of 10 plus 5*sq rt of 2 in surd form
-125
The numbers are: -5 +10 times sq rt of 2 and -5 - 10 times the sq rt of 2
The numbers are: -(1+sq rt 5)/2 and (-1+sq rt 5)/2
120
There are none because the numbers are: 2+sq rt of 11 and 2-sq rt of 11
The numbers are: (-14 +sq rt 190) and (-14 -sq rt 190) Check: (-14 +sq rt 190)+(-14 -sq rt 190) = -28 and (-14 +sq rt 190)*(-14 -sq rt 190) = 6
5 sq rt of 2
(1/sq rt 5)((1+sq rt 5)/2)n - (1/sq rt 5)((1-sq rt 5)/2)n This is based on the golden ratio (1+sq rt 5)/2) because the ratio of 2 Fibonacci terms approaches the golden ratio as the 2 terms used get larger. IE the ratio ot the 10th term to the 9th term is 55/34 = 1.61765 and the golden ratio is approx. 1.61803. When using this formula if your calculator does not round, you will round to get the appropriate Fibonacci number.
The numbers are: -2 +2*sq rt 19 and -2 -2*sq rt 19 Check: (-2 +2*sq rt 19)*(-2 -2*sq rt 19) = -72 and (-2 +2*sq rt 19)+(-2 -2*sq rt 19) = -4