Question

Обчислити 62: (9-√19)+4: (√23+√19) – 7: (√23+4)

Answer 1

$\displaystyle \frac{62}{9-\sqrt{19}} +\frac{4}{\sqrt{23}+\sqrt{19}} -\frac{7}{\sqrt{23}+4} =\\\\\\ =\frac{62(9+\sqrt{19})}{(9-\sqrt{19})(9+\sqrt{19})} +\frac{4(\sqrt{23}-\sqrt{19})}{(\sqrt{23}+\sqrt{19})(\sqrt{23}-\sqrt{19})} -\frac{7(\sqrt{23}-4)}{(\sqrt{23}+4)(\sqrt{23}-4)} = \\\\\\ =\frac{62(9+\sqrt{19})}{81-19} +\frac{4(\sqrt{23}-\sqrt{19})}{23-19} -\frac{7(\sqrt{23}-4)}{23-16}= \\\\\\ =\frac{62(9+\sqrt{19})}{62} +\frac{4(\sqrt{23}-\sqrt{19})}{4} -\frac{7(\sqrt{23}-4)}{7}=$

$=9+\sqrt{19}+\sqrt{23}-\sqrt{19}-(\sqrt{23}-4) =9+\sqrt{23}-\sqrt{23}+4= 13$

Answer 2

Вот так вот легко решается

Answer 3

To calculate the expression, follow these steps:

Step 1: Evaluate the expressions inside parentheses and square roots. Step 2: Perform the division operations. Step 3: Perform the addition and subtraction operations.

Let's go through each step:

Step 1:

• √19 ≈ 4.3589 (rounded to four decimal places)
• √23 ≈ 4.7958 (rounded to four decimal places)

Step 2:

• (9 - √19) ≈ (9 - 4.3589) ≈ 4.6411 (rounded to four decimal places)
• (4 / (√23 + √19)) ≈ (4 / (4.7958 + 4.3589)) ≈ 0.5344 (rounded to four decimal places)
• (7 / (√23 + 4)) ≈ (7 / (4.7958 + 4)) ≈ 0.6574 (rounded to four decimal places)

Step 3:

• 62 + 4.6411 + 0.5344 - 0.6574 ≈ 66.5181 (rounded to four decimal places)

So, the result of the expression is approximately 66.5181.