If-6-3x-is-the-geometric-mean-between-the-integer-x-2-2-and-2-what-are-the-values-of-x-

Question Number 117082 by bobhans last updated on 09/Oct/20

If 6 - 3 x is the geometric mean between

the integer x^{2} + 2 and \bar{2} what are the

values of x ?

Answered by bemath last updated on 09/Oct/20

geometric mean \Rightarrow \sqrt{(x^{2} + 2) . 2} = 6 - 3 x

the equation valid for 6 - 3 x ⩾ 0

or x ⩽ 2 .

squaring both sides gives

{2 x}^{2} + 4 = {9 x}^{2} - 36 x + 36

{7 x}^{2} - 36 x + 32 = 0

(7 x - 8) (x - 4) = 0

{\begin{cases} x = \frac{8}{7} \leftarrow accept \\ x = 4 \leftarrow rejected \end{cases}

the value of x is \frac{8}{7} .

Commented by bemath last updated on 09/Oct/20

i think this question not consisten

because x = \frac{8}{7} not a integer

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