Question

√(3-√17)^2-√(√17-5)^2

Answer 1

Ответ:

3-крень17-корень17-5=-2-2корня из 17= -4корня из 17

Объяснение:

Answer 2

Let's simplify the expression step by step:

√(3-√17)^2 - √(√17-5)^2

First, we can simplify the squares within the square roots:

√(3-√17)^2 = √(3-√17)(3-√17) = √(9 - 6√17 + 17) = √(26 - 6√17)

√(√17-5)^2 = √(√17-5)(√17-5) = √(17 - 10√17 + 25) = √(42 - 10√17)

Now, we can substitute these simplified expressions back into the original expression:

√(26 - 6√17) - √(42 - 10√17)

Let's focus on simplifying the first square root term:

√(26 - 6√17) = √(a - 2√ab + b) [By recognizing a pattern]

Where a = 26, b = 17, and ab = 6√17.

Using this pattern, we can rewrite the square root as:

√(26 - 6√17) = √(√(26) - √(6√17))^2 = (√(26) - √(6√17))

Now, let's simplify the second square root term:

√(42 - 10√17) = √(c - 2√cd + d) [By recognizing a pattern]

Where c = 42, d = 17, and cd = 10√17.

Using this pattern, we can rewrite the square root as:

√(42 - 10√17) = √(√(42) - √(10√17))^2 = (√(42) - √(10√17))

Substituting these simplified expressions back into the original expression, we have:

(√(26) - √(6√17)) - (√(42) - √(10√17))

Now, let's simplify further by combining like terms:

√(26) - √(6√17) - √(42) + √(10√17)

This is the simplified form of the expression √(3-√17)^2-√(√17-5)^2.