Question

Find the value of x² - x+1 when x=√3 -1, in the form a+b√3 where a and b are integers​

Answer 1

Answer:

$6-3\sqrt{3}$

If you compare this to $a+b\sqrt{3}$, then $a=6$ and $b=-3$.

Step-by-step explanation:

We are given $x=\sqrt{3}-1$ and we are asked to find the value of $x^2-x+1$.

So we will need to find $x^2$.

$x=\sqrt{3}-1$

Square both sides:

$x^2=(\sqrt{3}-1)^2$

Expand using identity: $(x-a)^2=x^2-2ax+a^2$.

$x^2=(\sqrt{3})^2-2(\sqrt{3})(1)+1^2$

$x^2=3-2\sqrt{3}+1$

$x^2=4-2\sqrt{3}$

Let's go back to the full $x^2-x+1$.

$x^2-x+1$

$(4-2\sqrt{3})-(\sqrt{3}-1)+1$

$4-2\sqrt{3}-\sqrt{3}+1+1$

$6-3\sqrt{3}$

If you compare this to $a+b\sqrt{3}$, then $a=6$ and $b=-3$.