Question

what is the square of 1
prove it with rules
full eaxplained??​

Answer 1

A=a2

About

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted \square ABCD. Wikipedia

Area: (side)²

Perimeter: 4 x side

Number of vertices: 4

Number of edges: 4

Since each side of a square is the same, it can simply be the length of one side cubed. If a square has one side of 4 inches, the volume would be 4 inches times 4 inches times 4 inches, or 64 cubic inches. (Cubic inches can also be written in3.)

If we measure from one corner to the opposite corner diagonally (as shown by the red line), and then compare that distance to the opposite diagonal measurement (as depicted by the blue line), the two distances should match exactly. If they are equal, the assembly is square.

Answer 2

Step-by-step explanation:

Completing the Square

Say we have a simple expression like x2 + bx. Having x twice in the same expression can make life hard. What can we do?

Well, with a little inspiration from Geometry we can convert it, like this:

Completing the Square Geometry

As you can see x2 + bx can be rearranged nearly into a square ...

... and we can complete the square with (b/2)2

In Algebra it looks like this:

x2 + bx + (b/2)2 = (x+b/2)2

"Complete the Square"

So, by adding (b/2)2 we can complete the square.

And (x+b/2)2 has x only once, which is easier to use.

Keeping the Balance

Now ... we can't just add (b/2)2 without also subtracting it too! Otherwise the whole value changes.

So let's see how to do it properly with an example:

Start with: x^2 + 6x + 7

("b" is 6 in this case)

Complete the Square:

x^2 + 6x + (6/2)^2 + 7 - (6/2)^2

Also subtract the new term

Simplify it and we are done.

simplifies to (x+3)^2

The result:

x2 + 6x + 7 = (x+3)2 − 2

And now x only appears once, and our job is done!

A Shortcut Approach

Here is a quick way to get an answer. You may like this method.

First think about the result we want: (x+d)2 + e

After expanding (x+d)2 we get: x2 + 2dx + d2 + e

Now see if we can turn our example into that form to discover d and e

Example: try to fit x2 + 6x + 7 into x2 + 2dx + d2 + e

x^2 + (6x) + [7] matches x^2 + (2dx) + [d^2+e]

Now we can "force" an answer:

We know that 6x must end up as 2dx, so d must be 3

Next we see that 7 must become d2 + e = 9 + e, so e must be −2

And we get the same result (x+3)2 − 2 as above!

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