Question

1) x^2=81. 2) x^2=100. 3) x^2=0,25. 4) x^2=0,04. 5) 4x^2=9. 6) 16x^2=81. 7) 25x^=0. 8) -3x^2=0. 9) 2x^2=14. 10) 3x^2=21

Answer 1

1) x^2=81  ответ: -9; 9

2) x^2=100 ответ: -10; 10

3) x^2=0,25 ответ: -0.5; 0.5

4) x^2=0,04 ответ: -0.2; 0.2

5) 4x^2=9

x^2=4/9 ответ: -2/3; 2/3

6) 16x^2=81

x^2=81/16 ответ: 9/4; 9/4

7) 25x^2=0 ответ: 0

8) -3x^2=0 ответ: 0

9) 2x^2=14

x^2=7 ответ: -√7 ; √7

10) 3x^2=21

x^2=7 ответ: -√7 ; √7

Answer 2

To solve these quadratic equations for $x$, you can take the square root of both sides. Remember that there are usually two solutions for a quadratic equation, one for the positive square root and one for the negative square root. Here are the solutions for each equation:

1. $x^2 = 81$ $x = \pm 9$

2. $x^2 = 100$ $x = \pm 10$

3. $x^2 = 0.25$ $x = \pm 0.5$ (or $x = \pm \frac{1}{2}$)

4. $x^2 = 0.04$ $x = \pm 0.2$ (or $x = \pm \frac{1}{5}$)

5. $4x^2 = 9$ Divide both sides by 4: $x^2 = \frac{9}{4}$ $x = \pm \frac{3}{2}$

6. $16x^2 = 81$ Divide both sides by 16: $x^2 = \frac{81}{16}$ $x = \pm \frac{9}{4}$

7. $25x^2 = 0$ This equation has only one solution, which is $x = 0$.

8. $-3x^2 = 0$ This equation also has only one solution, which is $x = 0$.

9. $2x^2 = 14$ Divide both sides by 2: $x^2 = 7$ $x = \pm \sqrt{7}$

10. $3x^2 = 21$ Divide both sides by 3: $x^2 = 7$ $x = \pm \sqrt{7}$

So, these are the solutions for each of the given quadratic equations.