Question

1. Square a number and subtract 5
.​

Answer 1

Answer:

let us square the number 6

6 square is 36

let's subtract 5 from 36

36-5=31

Step-by-step explanation:

hope this helps you

Answer 2

Let’s start with a perfect square of 2
n
2
and add 5
5
to it. Now 5
5
itself is an odd number, and all odd numbers conform to 2+1
2
n
+
1
where
n
is an integer. So:

2+5
n
2
+
5
is the same as +2+1
n
+
2
n
+
1

In turn, when factored +2+1=(+1)2 or (+1)(+1)
n
+
2
n
+
1
=
(
n
+
1
)
2
or
(
n
+
1
)
(
n
+
1
)
So it does result in a perfect square here.
Now we can easily deduce what
n
is equal to because we know what 2+1
2
n
+
1
equals.

2+1=5
2
n
+
1
=
5


⟹(2+1)−1=5−1
⟹
(
2
n
+
1
)
−
1
=
5
−
1


⟹22=42
⟹
2
n
2
=
4
2


⟹=2
⟹
n
=
2


So we end up with 22+2(2)+1=4+5=9
2
2
+
2
(
2
)
+
1
=
4
+
5
=
9
, and also (2+1)(2+1)=32=9
(
2
+
1
)
(
2
+
1
)
=
3
2
=
9


But we can’t subtract 5
5
to get a perfect square from 2
n
2
if the value of remains consistent, and equalling 2. After all (−1)2=2−2+1
(
n
−
1
)
2
=
n
2
−
2
n
+
1
which is the same as 2−3.
n
2
−
3.
So:

(−1)2≠2−5
(
n
−
1
)
2
≠
n
2
−
5


2−5=(−1)2−2
n
2
−
5
=
(
n
−
1
)
2
−
2


Perfect squares follow a pattern of 2
n
2
equals the sum of all consecutive odd integers up to the ℎ
n
t
h
term. In other words:

1=12
1
=
1
2


1+3=22
1
+
3
=
2
2


1+3+5=32
1
+
3
+
5
=
3
2


1+3+5+7=42
1
+
3
+
5
+
7
=
4
2


1+3+5+7+9=52
1
+
3
+
5
+
7
+
9
=
5
2


…and so on