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If a (x,3),B(7,-1) and AB=5 units,find the possible values of x.​

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Final answer:

The possible values of x for a (x,3),B(7,-1) and AB=5 units are x = 2 or x = 12.

Step-by-step explanation:

To find the possible values of x, we need to calculate the distance between points A(x,3) and B(7,-1). We can use the distance formula, which is given by:

d = sqrt((x-7)^2 + (3-(-1))^2)

Simplifying and squaring both sides of the equation, we get:

d^2 = (x-7)^2 + (4)^2

Since we know that the distance AB is equal to 5 units, we can substitute d = 5 into the equation:

25 = (x-7)^2 + 16

Expanding and rearranging the equation, we find:

0 = x^2 - 14x + 24

Factoring the equation, we get:

0 = (x-2)(x-12)

Setting each factor equal to zero, we find:

x-2 = 0 or x-12 = 0

Therefore, the possible values of x are x = 2 or x = 12.

User Hamed Kamrava
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