Question

1)c²-0,25=02)81x²-121=03)--0,09+4x²=0пример:1)a²-4=a²-2²=(a-2)(a+2)​

Answer 1

1)

${c }^{2} = 0 + 0.25$

$c = \sqrt{0.25}$

$c = 0.5$

2)

$81 {x}^{2} = 0 + 121$

${x}^{2} = 121 \div 81$

$x = \sqrt{121 \div 81}$

$x = \frac{11}{9}$

$4 {x}^{2} = 0 + 0.09$

${x}^{2} = 0.09 \div 4$

$x = \sqrt{0.09 \div 4}$

$x = 0.3 \div 2$

$x = 1.5$

Answer 2

1)c²-0,25= с²-0,5²=(с-0,5)(с+0,5)

2)81x²-121= 9²х²-11² = (9х-11)(9х+11)

3)--0,09+4x² = 4х²-0,09 = 2²х²-0,3² = (2х-0,3)(2х+0,3)

Answer 3

1. c² - 0.25 = 0

Add 0.25 to both sides:

c² = 0.25

Take the square root of both sides:

c = ±0.5

So the solutions are c = 0.5 and c = -0.5.

2. 81x² - 121 = 0

Add 121 to both sides:

81x² = 121

Take the square root of both sides:

9x = ±11

Divide by 9:

x = ±11/9

So the solutions are x = 11/9 and x = -11/9.

3. -0.09 + 4x² = 0

Add 0.09 to both sides:

4x² = 0.09

Divide by 4:

x² = 0.0225

Take the square root of both sides:

x = ±0.15

So the solutions are x = 0.15 and x = -0.15.

Example:

a² - 4 = a² - 2² = (a - 2)(a + 2)

This example is already solved correctly. We can factor the expression a² - 4 using the difference of squares formula, which tells us that a² - 4 = (a - 2)(a + 2).