Question

Consider this equation. √x - 1 - 5 = x - 8 The equation has(two valid solutions, one valid solution) and(one extraneous solution, no extraneous solutions) A valid solution for x is(0, 4, 2, 5)​

Answer 1

The equation has 2 valid solutions; no extraneous solutions

The given equation is:

$\sqrt{x - 1} - 5= x - 8$

First, we determine the solutions

$\sqrt{x - 1} - 5= x - 8$

Add 5 to both sides

$\sqrt{x - 1} = x - 8 + 5$

$\sqrt{x - 1} = x - 3$

Square both sides

$x - 1 = (x - 3)^2$

Expand

$x - 1 = x^2- 3x - 3x + 9$

$x - 1 = x^2- 6x + 9$

Collect like terms

$x^2 - 6x - x + 9 + 1 = 0$

$x^2 - 7x + 10 = 0$

Expand again

$x^2 - 2x-5x + 10 = 0$

Factorize

$x(x - 2) -5(x -2)= 0$

Factor out x - 2

$(x - 5)(x -2)= 0$

Split

$x - 5=0$ or $x - 2 = 0$

$x= 5$ or $x = 2$

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

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https://brainly.com/question/2396830

Answer 2

Answer:

That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.

Step-by-step explanation:

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