60
Let the two numbers be represented by a and b.
Then, ab = 27 so b = 27/a.
And, a + b = 33 . . . substituting for b gives :-
a + (27/a) = 33 . . . .multiplying throughout by a
a² + 27 = 33a . . . . . . . .rearranging
a² - 33a + 27 = 0
Solving this quadratic equation either by completing the square of using the quadratic formula gives the answer a = 32.16046 and 0.83954 . One of these figures can be regarded as the value for b.
32.16046 + 0.83954 = 33.0
32.16046 x 0.83954 = 27.0
-33
19
33
30
169
95
33
3
29.5 you add all of the numbers up then divide that total by the total amount of numbers. so for this example its 27+28+30+33= 118/4= 29.5
The numbers are: 33 -7 times sq rt of 21 and 33 +7 times sq rt of 21
Express the numbers in prime factorisation in power form: 12 = 22 x 31 27 = 33 For gcf multiply together the lowest power of the common primes: gcf of 12 and 27 = 31 = 3 For LCM multiply together the highest power of all the primes (across the numbers): LCM of 12 and 27 = 22 x 33 = 108
The most reasonable way to solve this is to find the two greatest numbers that will add to 65. This is 32 and 33. So if we multiply 32 * 33, you will get 1056.