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NISA [10]
3 years ago
13

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?

SAT
2 answers:
Fittoniya [83]3 years ago
8 0

Answer:

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?  

-----

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

------------------------------------

k = sqrt(6)

Explanation:

Arte-miy333 [17]3 years ago
3 0

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 = \frac{+/-\sqrt{-4*1/3*-2} }{2/3} = 3\frac{+/-\sqrt{8/3} }{2}  = +/-3*\sqrt{2/3} = +/-\sqrt{6}

so k = \sqrt{6}

and we can write the equation as:

(1/3)(x - √6)(x +√6)

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