Question

The expression 1/3x^2-2 can be as 1/3(x-k)(x+k),where k is a positive constant.What is the value of k?

Answer 1

The expression 1/3x^2-2 can be rewritten as 1/3(x-k)(x+k),where k is a positive constant.What is the value of k?

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(1/3)x^2-2 = (1/3)(x^2 - 6) = (1/3)(x-sqrt(6)(x+sqrt(6))

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k = sqrt(6)

Step-by-step explanation:

Answer 2

Answer: k = √6

Explanation: We have the equation:

(1/3)x^2 - 2

and we want to write this in the form:

(1/3)(x - k)(x +k)

k and -k are the solutions of the equation:

(1/3)x^2 - 2 = 0

wich are

`+/- k = (+/-√(-4*1/3*-2) )/(2/3) = 3(+/-√(8/3) )/(2)  = +/-3*√(2/3) = +/-√(6)`

so k =
`√(6)`

and we can write the equation as:

(1/3)(x - √6)(x +√6)