Question

Найти значение выражения: (7-4√3)(2+√3)^2

Answer 1

Задавай вопрос, если что-то непонятно)

Answer 2

$(7-4 \sqrt3)(2+ \sqrt3)^2=(4-2*2* \sqrt3+3)(2+ \sqrt3)^2=\\=(2^2-2*2* \sqrt3+( \sqrt3)^2)(2+ \sqrt3)^2=(2- \sqrt3)^2*(2+ \sqrt3)^2=\\=((2- \sqrt3)(2+ \sqrt3))^2=(4-3)^2=1^2=1$
УДАЧИ ВАМ ВО ВСЁМ)))!!!

Answer 3

To find the value of the expression, let's simplify it step by step:

Step 1: Expand the squared term (2 + √3)^2 (2 + √3)^2 = (2 + √3)(2 + √3) = 2(2) + 2(√3) + √3(2) + √3(√3) = 4 + 2√3 + 2√3 + 3 (since √3 * √3 = 3) = 7 + 4√3

Step 2: Now, multiply (7 - 4√3) by (2 + √3)^2 (7 - 4√3)(2 + √3)^2 = (7 - 4√3)(7 + 4√3)

Now, we can use the formula (a - b)(a + b) = a^2 - b^2 to simplify further:

(7 - 4√3)(7 + 4√3) = 7^2 - (4√3)^2 = 49 - 16 * 3 = 49 - 48 = 1

So, the value of the expression (7 - 4√3)(2 + √3)^2 is 1.