Question

30ab+(3a-5b) вквадрате при a=вкорне 6,b=вкорне12

Answer 1

Решение задания смотри на фотографии

Answer 2

To find the value of the expression (30ab + (3a - 5b))^2 when a = √6 and b = √12, we need to substitute these values into the expression and then square the result.

Step 1: Substitute the values of a and b into the expression. a = √6 b = √12

30ab + (3a - 5b) = 30(√6)(√12) + (3√6 - 5√12)

Step 2: Simplify the expression. √6 * √12 = √(6 * 12) = √72 = √(36 * 2) = 6√2

30 * 6√2 = 180√2

3√6 - 5√12 = 3√6 - 5√(6 * 2) = 3√6 - 5√6 * √2 = (3 - 5√2)√6

Step 3: Substitute the simplified values back into the expression. 30ab + (3a - 5b) = 180√2 + (3 - 5√2)√6

Step 4: Square the entire expression. (180√2 + (3 - 5√2)√6)^2

Step 5: Expand the squared expression. (180√2)^2 + 2 * 180√2 * (3 - 5√2)√6 + ((3 - 5√2)√6)^2

Step 6: Simplify further. 180^2 * 2 + 2 * 180 * (3 - 5√2)√6 + (3 - 5√2)^2 * 6

Step 7: Calculate the values. 180^2 = 32400 (3 - 5√2)^2 = (3 - 5√2)(3 - 5√2) = 9 - 15√2 - 15√2 + 25 * 2 = 9 - 30√2 + 50

(3 - 5√2)√6 = (3√6 - 5√(6 * 2)) = (3√6 - 5√6 * √2) = (3 - 5√2)√6

So, the expression becomes: 32400 + 2 * 180 * (3 - 5√2)√6 + (9 - 30√2 + 50) * 6

Step 8: Continue simplifying. 32400 + 2 * 180 * (3 - 5√2)√6 + (9 * 6 - 30√2 * 6 + 50 * 6)

Step 9: Final calculation. 32400 + 2 * 180 * (3 - 5√2)√6 + (54 - 180√2 + 300)

Step 10: Simplify the expression one last time. 32400 + 2 * 180 * (3 - 5√2)√6 + 354 - 180√2

Now, we can calculate the final result:

32400 + 2 * 180 * (3 - 5√2)√6 + 354 - 180√2 ≈ 33306.142

So, the value of the expression (30ab + (3a - 5b))^2 when a = √6 and b = √12 is approximately 33306.142.