First, solve the corresponding equation \( w^2 -
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- \times 4 = 36
- Hence, the product of the roots is \(\boxed{36}\).
- Find all solutions to the inequality \( w^2 - 4w + 3 < 0 \).
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Now evaluate $g(f(2)) = g(3)$:
g(3) = \sqrt{3 + 4} = \sqrt{7}
oxed{\sqrt{7}}
Question: If $x + rac{1}{x} = 4$, what is the value of $x^2 + rac{1}{x^2}$?
Solution: Start with the identity:
\left(x + rac{1}{x}
ight)^2 = x^2 + 2 + rac{1}{x^2}
Substitute $x + rac{1}{x} = 4$:
4^2 = x^2 + 2 + rac{1}{x^2} \Rightarrow 16 = x^2 + rac{1}{x^2} + 2
Solve for $x^2 + rac{1}{x^2}$: