Question

If x = 2 + root(3), then find the value of {x(square) - 4x + 1}.

Answer 1

PLEASE REPLY ASAP. PLEASE. I've got an exam tomorrow.

Answer 2

Recall that when you expand a second degree binomial you get:
`square of the first term` plus
`twice the product of both terms` plus
`square of the second term`.

Example:\[\Large\rm (a+b)^2=a^2+2(ab)+b^2\]Let's see if we can apply this to our problem here :)

Answer 3

\[\Large\rm (\color{orangered}{x})^2-4(\color{orangered}{x})+1\]We want to evaulate this when, \(\Large\rm \color{orangered}{x=2+\sqrt{3}}\)

Answer 4

\[\Large\rm (\color{orangered}{2+\sqrt{3}})^2-4(\color{orangered}{2+\sqrt{3}})+1\]

Answer 5

So expanding the square gives us:\[\Large\rm 2^2+2(2\sqrt3)+(\sqrt3)^2-4(\color{orangered}{2+\sqrt{3}})+1\]Understand how I did that?
Square of the first, 2 times the product of both in the middle, and square of the second.

Answer 6

Distribute the -4 to each term in the orange.
Then combine like-terms.
Shouldn't be too bad :o

Answer 7

I really didn't understand. Could you be a little more clear. I understand that (x2 - 4x + 1) is an identity (x - 1)2.

Answer 8

`I understand that (x^2 - 4x + 1) is an identity (x - 1)^2.`
What does this mean? :o

Answer 9

\[\Large\rm x^2-4x+1 \ne (x-1)^2\]\[\Large\rm x^2-2x+1=(x-1)^2\]

Answer 10

NOW TRY TO SOLVE IT PLEASE.....