Question

(4x-3)^2-25x^2=0 два корня в ответе

Answer 1

Відповідь:

ответ на фото.

Answer 2

Ответ:

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Answer 3

To solve the equation (4x-3)^2 - 25x^2 = 0 and find the two roots, we can follow these steps:

1. Expand the square: (4x-3)^2 = (4x-3)(4x-3) = 16x^2 - 24x + 9. 2. Rewrite the equation: (16x^2 - 24x + 9) - 25x^2 = 0. 3. Combine like terms: 16x^2 - 24x + 9 - 25x^2 = 0. 4. Simplify: -9x^2 - 24x + 9 = 0.

Now, we have a quadratic equation in standard form: -9x^2 - 24x + 9 = 0. To find the roots, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -9, b = -24, and c = 9. Plugging these values into the quadratic formula, we get:

x = (-(-24) ± √((-24)^2 - 4(-9)(9))) / (2(-9))

Simplifying further:

x = (24 ± √(576 + 324)) / (-18) x = (24 ± √900) / (-18) x = (24 ± 30) / (-18)

Now, we can calculate the two possible values for x:

1. When we take the positive square root: x = (24 + 30) / (-18) x = 54 / (-18) x = -3

2. When we take the negative square root: x = (24 - 30) / (-18) x = -6 / (-18) x = 1/3

Therefore, the equation (4x-3)^2 - 25x^2 = 0 has two roots: x = -3 and x = 1/3.