2 ^ x + 1/(2 ^ x) = 4 , maka nilai 4 ^ 7 + 1/(4 ^ x) =

Given the equation:

\[
2^x + \frac{1}{2^x} = 4
\]

we want to find the value of:

\[
4^x + \frac{1}{4^x}
\]

### Step 1: Simplify the given equation
Let \( y = 2^x \). Thus, the equation becomes:

\[
y + \frac{1}{y} = 4
\]

Multiplying both sides by \( y \):

\[
y^2 + 1 = 4y
\]

This can be rearranged as:

\[
y^2 - 4y + 1 = 0
\]

### Step 2: Solve the quadratic equation
To solve for \( y \), use the quadratic formula:

\[
y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Substituting \( a = 1, b = -4, \) and \( c = 1 \):

\[
y = \frac{4 \pm \sqrt{16 - 4}}{2} = \frac{4 \pm \sqrt{12}}{2} = \frac{4 \pm 2\sqrt{3}}{2}
\]

\[
y = 2 \pm \sqrt{3}
\]

### Step 3: Find \( 4^x + \frac{1}{4^x} \)
Since \( 4^x = (2^x)^2 = y^2 \), we need to find:

\[
4^x + \frac{1}{4^x} = y^2 + \frac{1}{y^2}
\]

To simplify this, use the identity:

\[
\left(y + \frac{1}{y}\right)^2 = y^2 + \frac{1}{y^2} + 2
\]

Given \( y + \frac{1}{y} = 4 \), squaring both sides:

\[
4^2 = y^2 + \frac{1}{y^2} + 2
\]

\[
16 = y^2 + \frac{1}{y^2} + 2
\]

\[
y^2 + \frac{1}{y^2} = 14
\]

Thus, the value of \( 4^x + \frac{1}{4^x} \) is:

\[
\boxed{14}
\]

Would you like to explore this further, or do you have any other questions?

### Related Questions:
1. How do you solve quadratic equations using the discriminant?
2. What are other methods to simplify expressions involving powers and fractions?
3. Can you explain the relationship between exponents and logarithms?
4. How do you find values of expressions involving multiple exponent rules?
5. How can you use substitution to simplify complex algebraic equations?

**Tip:** When solving equations with exponents, look for patterns or ways to simplify using algebraic identities!

2 ^ x + 1/(2 ^ x) = 4 , maka nilai 4 ^ x + 1/(4 ^ x) = ?

Learn how to solve the exponential equation 2^x + 1/(2^x) = 4 and find the value of 4^x + 1/(4^x). This step-by-step guide explores key concepts in algebra, exponential equations, and quadratic equations, suitable for students in Grades 9-11.

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