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Home » \( 12 = 2^2 \times 3^1 \) - Ready Digital AB

\( 12 = 2^2 \times 3^1 \) - Ready Digital AB

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 This confirms the expression is of the form $ a^2 - 2ab + b^2 = (a - b)^2 $:

📌 16x^2 - 40x + 25 = (4x - 5)^2

📌 Thus, the factored form is $ \boxed{(4x - 5)^2} $.

📌 Question: If $ x + \frac{1}{x} = 4 $, what is the value of $ x^2 + \frac{1}{x^2} $?

📌 We square both sides of the given equation:

📌 \left(x + \frac{1}{x}\right)^2 = 4^2 \Rightarrow x^2 + 2 + \frac{1}{x^2} = 16

📌 x^2 + \frac{1}{x^2} = 16 - 2 = 14

📌 Thus, the final answer is $ \boxed{14} $.

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e 0\). Then:
rac{x+y}{x-y} = rac{r+1}{r-1}.
Set this equal to each value of \(u\):
Case 1:** \( rac{r+1}{r-1} = rac{3 + \sqrt{5}}{2} \)
2(r+1) = (3 + \sqrt{5})(r - 1)
2r + 2 = (3 + \sqrt{5})r - (3 + \sqrt{5})
2r + 2 = (3 + \sqrt{5})r - 3 - \sqrt{5}
2r - (3 + \sqrt{5})r + 2 + 3 + \sqrt{5} = 0
r = rac{5 + \sqrt{5}}{1 + \sqrt{5}}
Rationalize:

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