Question

Решите уравнение: 1. (x-3)(x+3)-(8+x)²= -9
2. (x+2)²-x²=12
3. (x-6)²-x(x+8)=2
4. (x-7)²+3=(x-2)(x+2)
5. 2x²-x-1=x²-5x-(-1-x²) ​

Answer 1

$(x - 3)(x + 3) - (8 + x) {}^{2} = - 9 \\ x {}^{2} - 9 - x {}^{2} - 16x - 64 = - 9 \\ - 16x = 64 \\ x = 64 \div - 16 \\ x = - 4$

$(x + 2) {}^{2} - x {}^{2} = 12 \\ x {}^{2} + 4x + 4 - x {}^{2} = 12\\ 4x = 12 - 4 \\ 4x = 8 \\ x = 8 \div 4 \\ x = 2$

$(x - 6) {}^{2} - x(x + 8) = 2 \\ x {}^{2} - 12x + 36 - x {}^{2} - 8x = 2 \\ - 12x - 8x = 2 - 36 \\ - 20x = - 34 \\ x = - 34 \div - 20 \\ x = 1.7$

$(x - 7) {}^{2} + 3 = (x - 2)(x + 2) \\ x {}^{2} - 14x + 49 + 3 = x {}^{2} - 4 \\ - 14x = - 4 - 49 - 3 \\ - 14x = - 56 \\ x = - 56 \div - 14 \\ x = 4$