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The given problem is asking for the type of solutions for the quadratic equation:

\[
x^2 - 7x + 5 = 0
\]

We can determine the nature of the solutions by evaluating the discriminant, \( \Delta \), which is given by the formula:

\[
\Delta = b^2 - 4ac
\]

For the quadratic equation \( ax^2 + bx + c = 0 \), the coefficients are:

- \( a = 1 \)
- \( b = -7 \)
- \( c = 5 \)

Substituting these values into the discriminant formula:

\[
\Delta = (-7)^2 - 4(1)(5)
\]
\[
\Delta = 49 - 20
\]
\[
\Delta = 29
\]

Since \( \Delta > 0 \), this means that the quadratic equation has **two distinct real solutions**. 

Thus, the correct choice is:

\[
① \text{異なる２つの実数解をもつ (Two distinct real solutions)}
\]

Would you like more details on the solution process or have any questions?

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Here are 5 related questions to expand your understanding:
1. What happens when the discriminant \( \Delta = 0 \)?
2. How do we calculate the exact solutions using the quadratic formula?
3. Can a quadratic equation have complex solutions, and when?
4. How does changing the value of \( c \) affect the discriminant?
5. What are the graphical implications of a positive discriminant?

**Tip:** The discriminant not only tells the number of solutions but also whether they are real or complex.

次の2次方程式の解の種類を判別せよ。
2次方程式 x^2 - 7x + 5 = 0 は、ア。
① 異なる2つの実数解をもつ
② 重解をもつ
③ 異なる2つの虚数解をもつ

Learn how to determine the type of solutions for the quadratic equation x^2 - 7x + 5 = 0 using the discriminant method. This problem involves key algebraic concepts like quadratic equations and their discriminants, suitable for students in Grades 7-9.

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