Question

15.18 Найдите значение выражения а²-4а +3 при а=2+√3

Answer 1

=4+4√3+3-8-4√3+3=10-8=2

Answer 2

(2+корень из 3)во 2 -4а+3
2+1,7 во 2 -4*2+3
2 во 2 +2*2*1.7+1,7 во 2-4*2+3
4+6,8+2,89-4*2+3
13,69-8+3
8,69

Answer 3

To find the value of the expression $a^2 - 4a + 3$ when $a = 2 + \sqrt{3}$, we simply substitute the value of $a$ into the expression and perform the calculation:

$a^2 - 4a + 3 = (2 + \sqrt{3})^2 - 4(2 + \sqrt{3}) + 3$

Now, let's simplify step by step:

1. Square the term $2 + \sqrt{3}$: $(2 + \sqrt{3})^2 = (2 + \sqrt{3})(2 + \sqrt{3}) = 2^2 + 2\sqrt{3} + 2\sqrt{3} + \sqrt{3}^2 = 4 + 4\sqrt{3} + 3 = 7 + 4\sqrt{3}$

2. Distribute the $-4$ through the parentheses: $4(-2 - \sqrt{3}) = -8 - 4\sqrt{3}$

3. Finally, add the constant term $3$: $7 + 4\sqrt{3} - 8 - 4\sqrt{3} + 3 = 2$

Therefore, the value of the expression $a^2 - 4a + 3$ when $a = 2 + \sqrt{3}$ is $2$.