# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/7

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Question 7

---

## Exercise 7

### Question

export const metadata = {
  title: "Question 7",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

Given <InlineMath math="f(x) = x + 1" /> and <InlineMath math="(f(x))^2 = 5f(x) - 4" /> are satisfied by <InlineMath math="x_1" /> or <InlineMath math="x_2" />. What is the value of <InlineMath math="x_1 + x_2" />?


### Choices

- [ ] $$-6$$
- [ ] $$-3$$
- [ ] $$0$$
- [x] $$3$$
- [ ] $$6$$

### Answer & Explanation

export const metadata = {
  title: "Question 7 Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

We are given the equation <InlineMath math="(f(x))^2 = 5f(x) - 4" />. We can rearrange it into a quadratic equation in terms of <InlineMath math="f(x)" />:

<MathContainer>
  <BlockMath math="(f(x))^2 - 5f(x) + 4 = 0" />
</MathContainer>

This equation is satisfied by <InlineMath math="x_1" /> and <InlineMath math="x_2" />. Based on the sum of roots formula for quadratic equations (<InlineMath math="x_1 + x_2 = -\frac{b}{a}" />), the sum of the values of <InlineMath math="f(x)" /> satisfying the equation is:

<MathContainer>
  <BlockMath math="f(x_1) + f(x_2) = -\frac{-5}{1} = 5" />
</MathContainer>

Given <InlineMath math="f(x) = x + 1" />. We substitute this into the equation above:

<MathContainer>
  <BlockMath math="\begin{align*} (x_1 + 1) + (x_2 + 1) &= 5 \\ x_1 + x_2 + 2 &= 5 \\ x_1 + x_2 &= 5 - 2 \\ x_1 + x_2 &= 3 \end{align*}" />
</MathContainer>

Thus, the value of <InlineMath math="x_1 + x_2" /> is <InlineMath math="3" />.


---