The equation x + 2 = is of the form x + a = , where a, b, and c are all positive integers and b > 1. Using this equation as a model, create your own equation that has extraneous solutions. (Hint: Substitute 7 for x, and choose a value for a. Then square both sides so you can choose a, b, and c that will make the equation true.) (I know this is a handful but I'm really in need of help right now, thanks to everyone in advance!)

Extraneous solution for Equation x + 1 = √7x + 15 : x = - 2

Step-by-step explanation:

We are given the equation x + a = √bx + c. As the hint says, let's substitute 7 for x first, receiving the following equation.

7 + a = √7b + c

Now let's say a = 1 and c = 8. Through substitution we solve for b,

7 + 1 = √7b + 8

8 = √7b + 8

8² = (√7b + 8)²

64 = 7b + 8

7b = 64 - 8 = 56

b = 56 / 7 = 8

Therefore, the equation x + 1 = √8x + 8 ( substitute the value of b ) will have a solution of x = 7. Let's simplify this equation and see if we receive any extraneous solutions.

x + 1 = √8x + 8

(x + 1)² - (√8x + 8)² = 0

(x + 1)² - 8x + 8 = 0

(x + 1)² - 8(x + 1) = 0

(x + 1)(x + 1 - 8) = 0

(x + 1)(x - 7) = 0

x = - 1 and x = 7

We already know that x = 7, but x = - 1 is not an extraneous solution. Therefore let's simplify the equation x + 1 = √7x + 15 and see if we receive any extraneous solutions.

(x + 1)² - (√7x + 15)² = 0

(x + 1)² - 7x + 15 = 0

x² - 5x - 14 = 0

(x - 7)(x + 2) = 0

x = 7 and x = - 2

In this case x = - 2 is an extraneous solution. We can check by substituting it back into the equation x + 1 = √7x + 15.

- 2 + 1 = √7(- 2) + 15

- 1 = √- 14 + 15

- 1 = √1

- 1 ≠ 1 - hence proved that x = - 2 is our extraneous solution

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

3100

step-by-step explanation: