Question

1) (7-3Корень3)(3корень3+7) 3) (4корень3+2корень10)в квадрате 2)(4+корень3)в квадрате 4) (5+3корень3)квадрат -(3+5корень3)квадрат

Answer 1

1) 49-27=22

2) 19+8корень3

3) 88+16корень30

4) -32

Answer 2

Let's simplify each expression step by step:

1. (7 - 3√3)(3√3 + 7)

First, apply the distributive property (FOIL method): = 7 * 3√3 + 7 * 7 - 3√3 * 3√3 - 3√3 * 7 = 21√3 + 49 - 9 * 3 = 21√3 + 49 - 27 = 21√3 + 22

2. (4√3 + 2√10)^2

To square a binomial, use the formula: (a + b)^2 = a^2 + 2ab + b^2 = (4√3)^2 + 2 * 4√3 * 2√10 + (2√10)^2 = 16 * 3 + 16√30 + 40 = 48 + 16√30 + 40 = 88 + 16√30

3. (4 + √3)^2

= (4)^2 + 2 * 4 * √3 + (√3)^2 = 16 + 8√3 + 3 = 19 + 8√3

4. (5 + 3√3)^2 - (3 + 5√3)^2

Use the formula: (a + b)^2 - (c + d)^2 = (a^2 + 2ab + b^2) - (c^2 + 2cd + d^2) = (5)^2 + 2 * 5 * 3√3 + (3√3)^2 - (3)^2 - 2 * 3 * 5√3 - (5√3)^2 = 25 + 30√3 + 27 - 9 - 30√3 - 75 = 52 + 30√3 - 84 = -32 + 30√3

So, the simplified expressions are:

1. 21√3 + 22
2. 88 + 16√30
3. 19 + 8√3
4. -32 + 30√3