jayanti wrote:a positive integer x is multiplied by 2 and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x

x is multiplied by 2 = 2x
product is then divided by 3 = 2x/3, which is the result
√(2x/3) = x
2x/3 = x²
So, x² - 2x/3 = 0
x(x - 2/3) = 0
[spoiler]x = 0, 2/3, which is not possible [/spoiler]

jayanti wrote:a positive integer x is multiplied by 2 and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x

positive integer x is multiplied by 2 --> 2x

this product is then divided by 3 --> 2x/3

the positive square root of the result of these two operations equals x --> root[2x/3] = x

To solve for x, first square both sides --> 2x/3 = x^2

Multiply both sides by 3 --> 2x = 3x^2

This is a quadratic equation, so set the equation equal to zero --> 3x^2 - 2x = 0

Factor --> x(3x - 2) = 0

This means either x = 0 or 3x-2 = 0

x = 0 cannot be a solution since we are told that x is a positive integer

If 3x-2 = 0 then x = 2/3, but this cannot be a solution either since we are told that x is a positive integer

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