Để chứng minh rằng không tồn tại các số thực \( x, y, z \) thỏa mãn các phương trình đã cho, ta cần phân tích từng phương trình một cách chi tiết.

### Phương trình (a)
\[ x^2 + 4y^2 - z^2 - 2x - 6z + 8y + 15 = 0 \]

Ta sẽ hoàn thành bình phương cho từng biến.

1. **Biến \( x \)**:
\[ x^2 - 2x = (x-1)^2 - 1 \]

2. **Biến \( y \)**:
\[ 4y^2 + 8y = 4(y^2 + 2y) = 4((y+1)^2 - 1) = 4(y+1)^2 - 4 \]

3. **Biến \( z \)**:
\[ -z^2 - 6z = -(z^2 + 6z) = -((z+3)^2 - 9) = -(z+3)^2 + 9 \]

Thay vào phương trình ban đầu:
\[ (x-1)^2 - 1 + 4(y+1)^2 - 4 - (z+3)^2 + 9 + 15 = 0 \]

Đơn giản hóa:
\[ (x-1)^2 + 4(y+1)^2 - (z+3)^2 + 19 = 0 \]

Chuyển \( 19 \) sang vế phải:
\[ (x-1)^2 + 4(y+1)^2 - (z+3)^2 = -19 \]

Vì \( (x-1)^2 \geq 0 \), \( 4(y+1)^2 \geq 0 \), và \( -(z+3)^2 \leq 0 \), tổng của các số không âm và số âm không thể bằng một số âm (-19). Do đó, phương trình này không có nghiệm thực.

### Phương trình (b)
\[ x^2 + 26y^2 + 14x - 76y + 59 = 0 \]

Hoàn thành bình phương cho từng biến.

1. **Biến \( x \)**:
\[ x^2 + 14x = (x+7)^2 - 49 \]

2. **Biến \( y \)**:
\[ 26y^2 - 76y = 26(y^2 - \frac{76}{26}y) = 26(y^2 - \frac{38}{13}y) = 26((y - \frac{38}{26})^2 - (\frac{38}{26})^2) = 26((y - \frac{19}{13})^2 - \frac{361}{169}) = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13})^2 - 26 \cdot \frac{361}{169} = 26(y - \frac{19}{13