2 + root 5 by minus 254 squared minus 2 minus 5 + 2 + 5 whole square
The Correct Answer and Explanation is:
Let’s break down the given expression step by step:
The expression is: 2+5(−254)2−(2−5+2+5)2\frac{2 + \sqrt{5}}{(-254)^2} – (2 – 5 + 2 + 5)^2(−254)22+5−(2−5+2+5)2
Step 1: Simplify the numerator in the first term
2+52 + \sqrt{5}2+5
This is already in its simplest form, so we leave it as is.
Step 2: Simplify the denominator in the first term
The denominator is (−254)2(-254)^2(−254)2, so we calculate: (−254)2=64516(-254)^2 = 64516(−254)2=64516
Thus, the first term becomes: 2+564516\frac{2 + \sqrt{5}}{64516}645162+5
Step 3: Simplify the second term inside the parentheses
The second term is (2−5+2+5)2(2 – 5 + 2 + 5)^2(2−5+2+5)2. Let’s first simplify inside the parentheses: 2−5+2+5=42 – 5 + 2 + 5 = 42−5+2+5=4
Now, square the result: 42=164^2 = 1642=16
Thus, the second term becomes: 161616
Step 4: Combine the two terms
Now, the expression becomes: 2+564516−16\frac{2 + \sqrt{5}}{64516} – 16645162+5−16
At this point, we can compute a decimal approximation for the first term. We know that 5≈2.236\sqrt{5} \approx 2.2365≈2.236, so: 2+5≈2+2.236=4.2362 + \sqrt{5} \approx 2 + 2.236 = 4.2362+5≈2+2.236=4.236
Now, divide by 64516: 4.23664516≈6.57×10−5\frac{4.236}{64516} \approx 6.57 \times 10^{-5}645164.236≈6.57×10−5
So, the expression becomes: 6.57×10−5−166.57 \times 10^{-5} – 166.57×10−5−16
Now, subtract: 6.57×10−5−16≈−15.99993436.57 \times 10^{-5} – 16 \approx -15.99993436.57×10−5−16≈−15.9999343
Final Answer:
−15.9999343-15.9999343−15.9999343
This is the approximate value of the expression. Since the first term is so small compared to the second term, it has almost no effect on the final result.
