Question

Обчисліть: (3√7-2√6)²=

Answer 1

(3√7-2√6)²=9*7+4*6-2*3√7*2√6=63+24-12√42=87-12√42

Answer 2

To compute the square of the expression (3√7 - 2√6)², we'll follow these steps:

Step 1: Expand the square of the expression. Step 2: Simplify the terms.

Step 1: (3√7 - 2√6)² = (3√7 - 2√6)(3√7 - 2√6)

Step 2: Using the FOIL method (First, Outer, Inner, Last), we multiply the terms:

(3√7 * 3√7) + (3√7 * -2√6) + (-2√6 * 3√7) + (-2√6 * -2√6)

Now, calculate each term:

1. (3√7 * 3√7) = 3^2 * (√7)^2 = 9 * 7 = 63
2. (3√7 * -2√6) = -2 * 3 * √(7 * 6) = -6√42
3. (-2√6 * 3√7) = -2 * 3 * √(6 * 7) = -6√42
4. (-2√6 * -2√6) = -2^2 * (√6)^2 = 4 * 6 = 24

Now, put everything together:

(3√7 - 2√6)² = 63 - 6√42 - 6√42 + 24

Combine like terms:

(3√7 - 2√6)² = 63 - 12√42 + 24

The final result is:

(3√7 - 2√6)² = 87 - 12√42