Question

Решите уравнение: 1) (a-8)(a+12)=0 2) m^2-0,25=0 3) 9x^2-64=0 4) b^2+36=0 5) 4x^2-9=0 6) x^2-16=0 7) 1/2-y^2=0 8) x^2-9/25=0 9) 81a^2+1=0 10) 49/81m^2-1=0

Answer 1

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Answer 2

1. (a-8)(a+12) = 0 Setting each factor to zero gives: a-8 = 0 or a+12 = 0 Solving each equation for a, we get: a = 8 or a = -12 Therefore, the solutions are a = 8 or a = -12.

2. m^2-0.25=0 Adding 0.25 to both sides, we get: m^2 = 0.25 Taking the square root of both sides (remembering to consider both the positive and negative roots), we get: m = 0.5 or m = -0.5 Therefore, the solutions are m = 0.5 or m = -0.5.

3. 9x^2-64=0 Adding 64 to both sides, we get: 9x^2 = 64 Taking the square root of both sides (remembering to consider both the positive and negative roots), we get: x = 8/3 or x = -8/3 Therefore, the solutions are x = 8/3 or x = -8/3.

4. b^2+36=0 Subtracting 36 from both sides, we get: b^2 = -36 Since the square of any real number is non-negative, there are no real solutions to this equation.

5. 4x^2-9=0 Adding 9 to both sides, we get: 4x^2 = 9 Taking the square root of both sides (remembering to consider both the positive and negative roots), we get: x = 3/2 or x = -3/2 Therefore, the solutions are x = 3/2 or x = -3/2.

6. x^2-16=0 Adding 16 to both sides, we get: x^2 = 16 Taking the square root of both sides (remembering to consider both the positive and negative roots), we get: x = 4 or x = -4 Therefore, the solutions are x = 4 or x = -4.

7. 1/2-y^2=0 Adding y^2 to both sides and multiplying by 2, we get: 1 = 2y^2 Dividing both sides by 2 and taking the square root (remembering to consider both the positive and negative roots), we get: y = 1/sqrt(2) or y = -1/sqrt(2) Therefore, the solutions are y = 1/sqrt(2) or y = -1/sqrt(2).

8. x^2-9/25=0 Adding 9/25 to both sides, we get: x^2 = 9/25 Taking the square root of both sides (remembering to consider both the positive and negative roots), we get: x = 3/5 or x = -3/5 Therefore, the solutions are x = 3/5 or x = -3/5.

9. 81a^2+1=0 Subtracting 1 from both sides and dividing by 81, we get: a^2 = -1/81 Since the square of any real number is non-negative, there are no real solutions to this equation.

10. 49/81m^2-1=0 Adding 1 to both sides and multiplying by 81/49, we get: m^2 =