Question

Решите уравнение ((√x)-3)*(x^2 + 4x -21) = 0

Answer 1

$( \sqrt{x} - 3)( {x}^{2} + 4x - 21) = 0$
Произведение равно нулю, если хотя бы один из множителей равен 0.
$\sqrt{x} - 3 = 0 \\ \sqrt{x} = 3 \\ x = 9$
или
х^2 + 4х - 21 = 0
D = b^2 - 4ac = 16 - 4*(-21) = 100
x1 = (-4 + 10)/2 = 6/2 = 3
x2 = (-4 - 10)/2 = -14/2 = -7

Ответ: -7; 3; 9.

Answer 2

To solve the equation ((√x) - 3) * (x^2 + 4x - 21) = 0, we need to find the values of x that satisfy the equation. To do this, we'll set each factor to zero and solve for x:

1. (√x) - 3 = 0
2. x^2 + 4x - 21 = 0

Let's solve each equation step by step:

1. (√x) - 3 = 0

Add 3 to both sides:

√x = 3

Square both sides to eliminate the square root:

x = 3^2

x = 9

Now, let's solve the second equation:

2. x^2 + 4x - 21 = 0

This is a quadratic equation, and we can solve it using factoring or the quadratic formula. Since it factors nicely, let's factor it:

(x + 7)(x - 3) = 0

Now, set each factor to zero:

x + 7 = 0 or x - 3 = 0

Solve for x:

1. x + 7 = 0

Subtract 7 from both sides:

x = -7

2. x - 3 = 0

Add 3 to both sides:

x = 3

So, the values of x that satisfy the equation are x = 9, x = -7, and x = 3.