Just divide the number that is biggest by 2 and you should get the answers for example #1 10÷2=5, #2 1÷2=0.5 #3 0.01÷2=0.005
In this problem, it is important to take note that the number of numbers to be utilized isn't specified so it can be up to a thousand numbers. It wasn't also specified if repeating of numbers is allowed or not. So with those taken into consideration and the condition presented in mind, the numbers that can give you 8 when added and 30 when multiplied are 2, 3, 5, -1, and another -1. The derivation from this is mainly from factorization and a little bit of logic.
here is the solution.
2 x 3 x 5 x -1 x -1 = 30
6 x 5 x -1 x -1 = 30
30 x -1 x -1 = 30
-30 x -1 = 30
30 = 30
2 + 3 + 5 + -1 + -1 = 8
5 + 5 + -1 + -1 = 8
10 + -1 + -1 = 8
9 + -1 = 8
8 = 8
Three hundred and six thousandths :)
You can know a perfect square trinomial:
i) if the coefficient of a² = 1.
ii) If you divide the middle number coefficient by 2 and you square it you get the last term.
Take for example the first option:
For all the options, the coefficient of a² = 1
a² + 4a + 16.
Coefficient of a = 4.
4/2 = 2
2² = 4, this does not equal the last term so it is not a perfect square trinomial.
a² + 14a + 49.
Coefficient of a = 14.
14/2 = 7
7² = 49, this is equal the last term so it is a perfect square trinomial.
And the perfect square is (a +7)²
Similarly if you test the last option.
a² + 26a + 169.
Coefficient of a = 26.
26/2 = 13
13² = 169, this is equal the last term so it is a perfect square trinomial.
And the perfect square is (a +13)²
So the only two options are: a² + 14a + 49 and a² + 26a + 169.
Other options do not pass this test.
