Question

9−3√​5​​​​​ / (√​3​​​−√​15​​​)​^2​​

Answer 1

(9-3√5)/(√3-√15)²=
3(3-√5)/(3-2√45+15)=
3(3-√5)/(18-6√5)=3(3√5)/6(3-√5)=
3/6=1/2

Answer 2

Ответ: 0,5.

Answer 3

We can begin by simplifying the denominator first:

(√3−√15)² = (3 - 2√3√15 + 15) = 18 - 6√5

So, the expression becomes:

9−3√5 / (18 - 6√5)

We can simplify this by dividing both numerator and denominator by 3:

3 - √5 / (6 - √5)

To rationalize the denominator, we can multiply both numerator and denominator by the conjugate of the denominator:

(3 - √5)(6 + √5) / [(6 - √5)(6 + √5)]

Simplifying the numerator:

(3 * 6) + (3 * √5) - (6 * √5) - (√5 * √5) = 18 - 3√5 - 5 = 13 - 3√5

Simplifying the denominator:

(6 * 6) - (√5 * √5) = 36 - 5 = 31

So the final simplified expression is:

(3 - √5)(6 + √5) / (36 - 5) = (3 - √5)(6 + √5) / 31

Or

(18 + 3√5 - 6√5 - 5) / 31 = (13 - 3√5) / 31

Therefore, 9−3√5 / (√3−√15)² simplifies to (13 - 3√5) / 31.