Question

( 4x² - 7x + 3 ) √5x+6 = 0

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the equation (4x² - 7x + 3)√(5x + 6) = 0, you can use the zero product property, which states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero.

In this case, we have:

(4x² - 7x + 3)√(5x + 6) = 0

Now, to find the solutions, set each factor to zero and solve for x:

1. 4x² - 7x + 3 = 0

To factor this quadratic equation, we look for two numbers whose product is equal to the product of the first and last coefficients (4 * 3 = 12) and whose sum is equal to the middle coefficient (-7).

The two numbers are -3 and -4.

So, we can factor the equation as follows:

(2x - 3)(2x - 1) = 0

Now, set each factor to zero and solve for x:

2x - 3 = 0 => 2x = 3 => x = 3/2

2x - 1 = 0 => 2x = 1 => x = 1/2

2. √(5x + 6) = 0

To solve for x in this equation, we isolate the square root by squaring both sides:

(√(5x + 6))² = (0)²

5x + 6 = 0

Subtract 6 from both sides:

5x = -6

Finally, divide by 5:

x = -6/5

So the solutions to the equation are:

x = 3/2, x = 1/2, x = -6/5.