Question

√3-√2/ (4√3+4√2) четверки над корнем

Answer 1

Решение во вложении :)))))

Answer 2

To simplify the expression, we need to rationalize the denominator, which means getting rid of the square root from the denominator. To do this, we can multiply both the numerator and the denominator by the conjugate of the denominator.

The conjugate of the denominator is obtained by changing the sign between the two terms with the square roots. So for the expression (4√3 + 4√2), the conjugate is (4√3 - 4√2).

Now, let's perform the multiplication:

[√3 - √2] / [4√3 + 4√2]

Multiply both the numerator and the denominator by the conjugate (4√3 - 4√2):

([√3 - √2] * [4√3 - 4√2]) / ([4√3 + 4√2] * [4√3 - 4√2])

Expanding the numerator and the denominator:

[4√3√3 - 4√3√2 - 4√2√3 + 4√2√2] / [16√3√3 - 16√3√2 + 16√2√3 - 16√2√2]

Simplifying:

[4√9 - 4√6 - 4√6 + 4√4] / [16√9 - 16√6 + 16√6 - 16√4]

√9 is simply 3, and √4 is 2:

[4 * 3 - 2 * 4√6] / [16 * 3 - 16 * 2]

Simplifying further:

[12 - 8√6] / [48 - 32]

Now, simplify the denominator:

[12 - 8√6] / 16

And the final result is:

(12 - 8√6) / 16

You can leave the answer as it is, or you can simplify it further by dividing both the numerator and denominator by 4:

(3 - 2√6) / 4