Question

2¹/2-2¹/⁴d=7⁹/16

Answer 1

To solve the equation \( 2^{1/2} - 2^{1/4} d = \frac{7^{9/16}} \), let's first simplify the equation step by step.

1. **Rewrite the exponents**:
- \( 2^{1/2} \) is the same as \( \sqrt{2} \).
- \( 2^{1/4} \) is the same as \( \sqrt[4]{2} \).

2. **Rearrange the equation**:
\[
2^{1/2} - \frac{7^{9/16}}{2^{1/4}} = d
\]

3. **Find \( 2^{1/2} \) and \( 2^{1/4} \)**:
- \( 2^{1/2} = \sqrt{2} \).
- \( 2^{1/4} = \sqrt[4]{2} \).

4. **Convert the equation**:
We can express everything using approximate numerical values or just keep them in terms of exponents.

Now, without full numerical simplifications, let’s isolate \( d \):

\[
d = 2^{1/2} - 2^{1/4} d \implies d + 2^{1/4} d = 2^{1/2}
\]
\[
d(1 + 2^{1/4}) = 2^{1/2}
\]
\[
d = \frac{2^{1/2}}{1 + 2^{1/4}}
\]

Next, to find \( d \) explicitly using numerical values if needed, you can calculate \( 2^{1/2} \), \( 2^{1/4} \), and substitute to find \( d \).

Assuming you meant to find just \( d \), we can isolate it or evaluate \( d \) numerically based on real values:

1. Approximate \( 2^{1/2} \approx 1.4142 \)
2. Approximate \( 2^{1/4} \approx 1.1892 \)

From here, simply substitute those values to compute \( d \):

\[
d \approx \frac{1.4142}{1 + 1.1892} \approx \frac{1.4142}{2.1892}.
\]
Now calculating it gives:

\( d \approx 0.6455 \).

To summarize, the value of \( d \) will present as:

\[
d \approx 0.6455.
\]
If you meant something different with the notation of the equation, please clarify further for specific steps!