Question

49^1+√‎2*7^1-√‎2*7^-2-√‎2

Answer 1

$49^{1+\sqrt{2}}*7^{1-\sqrt{2}}*7^{-2-\sqrt{2}}=(7^{2})^{1+\sqrt{2}}*7^{1-\sqrt{2} }*7^{-2-\sqrt{2}}=7^{2+2\sqrt{2}}*7^{1-\sqrt{2}}*7^{-2-\sqrt{2}}=7^{2+2\sqrt{2}+1-\sqrt{2}-2-\sqrt{2}}=7$

Answer 2

Let's break down the expression step by step:

49^1 = 49

√‎2 * 7^1 = √‎2 * 7 = 7√‎2

√‎2 * 7^-2 = √‎2 * (1/7^2) = √‎2 * (1/49) = √‎2/49

Finally, combining all the terms:

49 + 7√‎2 - √‎2/49 - √‎2

To simplify further, we can combine the terms with √‎2:

49 - √‎2/49 + 7√‎2 - √‎2

Next, we can combine the whole number terms:

49 + 7√‎2 - √‎2/49 - √‎2

Now, we have terms with and without √‎2. Let's combine them:

49 - √‎2/49 + 7√‎2 - √‎2 = 49 + 7√‎2 - √‎2/49 - √‎2

Finally, we can simplify the expression:

49 + 7√‎2 - √‎2/49 - √‎2 ≈ 49 + 7√‎2 - 0.0204 - √‎2 ≈ 49 + 6√‎2 - 0.0204

Please note that the approximation is given since the exact value of √‎2/49 is a decimal.