Question

(x-2)(x+5)*√x^2 - 9=0

Answer 1

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Answer 2

To solve the equation $(x-2)(x+5)\sqrt{x^2 - 9} = 0$, we can first apply the zero-product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. In this case, we have three factors:

1. $(x-2)$
2. $(x+5)$
3. $\sqrt{x^2 - 9}$

So, we can set each factor equal to zero and solve for $x$:

1. $x - 2 = 0$ Add 2 to both sides: $x = 2$

2. $x + 5 = 0$ Subtract 5 from both sides: $x = -5$

3. $\sqrt{x^2 - 9} = 0$ Square both sides to eliminate the square root: $x^2 - 9 = 0$

Now, solve for $x$ by adding 9 to both sides:

$x^2 = 9$

Take the square root of both sides (don't forget both positive and negative roots):

$x = ±3$

So, the solutions to the equation $(x-2)(x+5)\sqrt{x^2 - 9} = 0$ are $x = 2$, $x = -5$, $x = 3$, and $x = -3$.