Question

Solve the equation 9x4=25x2

Answer 1

$9 {x}^{4} = 25 {x}^{2} \\ {3}^{2} {x}^{4} - {5}^{2} {x}^{2} = 0 \\ {x}^{2} ( {(3x)}^{2} - {5}^{2} ) = 0 \\ {x}^{2} (3x - 5)(3x + 5) = 0 \\ {x}^{2} = 0 \\ x = 0 \\ 3x - 5 = 0 \\ x = \frac{5}{3} = 1 \frac{2}{3} \\ 3x + 5 = 0 \\ x = - 1 \frac{2}{3}$

Ответ: – 1⅔, 0, 1⅔.

Answer 2

Ответ: x1=0, x2=5/3, x3=-5/3.

Объяснение:

Answer 3

To solve the equation 9x^4 = 25x^2, we can rearrange the equation and set it equal to zero:

9x^4 - 25x^2 = 0

Now, we can factor out common terms:

x^2(9x^2 - 25) = 0

Next, we apply the zero product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:

x^2 = 0 or 9x^2 - 25 = 0

For x^2 = 0, taking the square root of both sides gives us:

x = 0

For 9x^2 - 25 = 0, we can factor the quadratic equation:

(3x)^2 - 5^2 = 0

Using the difference of squares identity (a^2 - b^2 = (a + b)(a - b)), we have:

(3x + 5)(3x - 5) = 0

Setting each factor equal to zero:

3x + 5 = 0 or 3x - 5 = 0

Solving for x in each equation:

3x + 5 = 0: 3x = -5 x = -5/3

3x - 5 = 0: 3x = 5 x = 5/3

Therefore, the solutions to the equation 9x^4 = 25x^2 are x = 0, x = -5/3, and x = 5/3.