Question

Решите (7√3+√48-√75)*√3 (6-√5)(2+7√5) (5√2+6√3)(6√2-5√3) (√17-√11)(√17+√11) (2√x-5√y)(2√x+5√y) (√6-2)^2 (3√7-2√3)^2

Answer 1

(7√3+√48-√75)*√3=(7√3+4√3-5√3)√3=6√3*√3=18

(6-√5)(2+7√5)=12-2√5+42√5-35=40√2-23

(5√2+6√3)(6√2-5√3)=5*6*2+36√6-25√6-90=11√6-30

(√17-√11)(√17+√11)=17-11=6

(2√x-5√y)(2√x+5√y)=2*2*х-5*5*у=4х-25у

(√6-2)^2=6-4√6+4=10-4√6

(3√7-2√3)^2=3*3*7-2*3√21-2*3*√21-2*2*3=

=75-12√21

Answer 2

To solve the given expression, we'll simplify it step by step. Let's start:

1. Simplify the expressions inside the parentheses first:

√48 = √(16 * 3) = √16 * √3 = 4√3 √75 = √(25 * 3) = √25 * √3 = 5√3

2. Now, replace these values in the original expression:

(7√3 + 4√3 - 5√3) * √3 (6 - √5)(2 + 7√5) (5√2 + 6√3)(6√2 - 5√3) (√17 - √11)(√17 + √11) (2√x - 5√y)(2√x + 5√y) (√6 - 2)^2 (3√7 - 2√3)^2

3. Combine like terms inside the first set of parentheses:

(7√3 + 4√3 - 5√3) = 6√3

4. Now, simplify the first set of parentheses:

6√3 * √3 = 6√3 * √3 = 6 * 3 = 18

5. Simplify the other pairs of parentheses:

(6 - √5)(2 + 7√5) = 6 * 2 + 6 * 7√5 - √5 * 2 - √5 * 7√5 = 12 + 42√5 - 2√5 - 7√5 * √5 = 12 + 42√5 - 2√5 - 7√(5^2) = 12 + 42√5 - 2√5 - 7 * 5 = 12 + 42√5 - 2√5 - 35 = -23 + 40√5

(5√2 + 6√3)(6√2 - 5√3) = 5√2 * 6√2 + 5√2 * (-5√3) + 6√3 * 6√2 + 6√3 * (-5√3) = 30√2 + (-25√6) + 36√6 + (-30√3) = 30√2 + 36√6 - 25√6 - 30√3 = 30√2 + 11√6 - 30√3

(√17 - √11)(√17 + √11) = (√17)^2 - (√11)^2 = 17 - 11 = 6

(2√x - 5√y)(2√x + 5√y) = (2√x)^2 - (5√y)^2 = 4x - 25y

(√6 - 2)^2 = (√6)^2 - 2 * √6 * 2 + 2^2 = 6 - 4√6 + 4 = 10 - 4√6

(3√7 - 2√3)^2 = (3√7)^2 - 2 * 3√7 * 2√3 + (2√3)^2 = 9 * 7 - 12√21 + 4 * 3 = 63 - 12√21 + 12 = 75 - 12√21

6. Finally, multiply all the simplified expressions:

18 * (-23 + 40√5) * (30√2 + 11√6 - 30√3) * 6 * 4x - 25y * 6 * (10 - 4√6) * (75 - 12√21)

Now, you can perform further calculations or leave the expression in this factored form.