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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink]
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priteshsad wrote:
2/9 ?


Nope. The question comes down to (3x)^ 1/6 = (2x) ^ 1/4

so 3x = (2x) ^6/4 or (2x)^2
3x = 4x^2
x = 3/4
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink]
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it stands for (3x)^ 1/8 = (2x) ^ 1/4 ,
so 3x=(2x)^1/2,
3x=4*x^2
x=3/4
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If \sqrt * \sqrt* \sqrt 3x [#permalink]
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If \(\sqrt{\sqrt{\sqrt{3x}}} = \sqrt[4]{2x}\) , what is the greatest possible value of x?

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0.75
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink]
could someone explain in more detail?
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If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink]
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\(3x^{\frac{1}{8}}= 2x^{\frac{1}{4}}\)

When both sides are raised to the fourth power

\(\sqrt{3x} = 2x\)

Squaring both the sides

\(3x = 4x^2\)

\(4x^2 - 3x = 0\)

\(x(x - \frac{3}{4}) = 0\)

\(x = 0 / \frac{3}{4}\)

Greatest possible value \(= \frac{3}{4}\)

Samamammadova8888 wrote:
could someone explain in more detail?
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Re: If √√√(3x) = 4√(2x), what is the greatest possible value of [#permalink]
Thanks for the explanation!
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If \sqrt * \sqrt* \sqrt 3x [#permalink]
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\(\sqrt{\sqrt{\sqrt{3x}}} = ^{4}\sqrt{2x}\)

\(((3x^{\frac{1}{2}})^{\frac{1}{2}})^{\frac{1}{2}} = 2x^{\frac{1}{4}}\)

\(3x^{\frac{1}{2}*\frac{1}{2}*\frac{1}{2}} = 2x^{\frac{1}{4}}\)

\(3x^{\frac{1}{8}} = 2x^{\frac{1}{4}}\)

\((3x^{\frac{1}{8}})^{8} = (2x^{\frac{1}{4}})^{8}\)

\(3x = 4x^{2}\)

\(4x^{2} - 3x = 0\)

\(x(4x - 3) = 0\)

\(x = 0 \) and \(\frac{3}{4}\)

Greatest value of \(x = \frac{3}{4} = \)0.75
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If (3x) = 4(2x), what is the greatest possible value of [#permalink]
\(\sqrt{\sqrt{\sqrt{3x}\) = \(\sqrt[4]{2x}\)

Squaring both sides

\(\sqrt{\sqrt{3x\) = \(\sqrt[2]{2x}\)

Squaring both sides again

\(\sqrt{3x} = 2x\)

Squaring both sides again ( I know its kinda getting....., but hold on!)

\(3x = 2^2x^2\)

\(3x = 4x^2\)

\(4x^2 - 3x = 0\)

Factoring \(2x\) out

\(2x(2x-\frac{3}{2}) = 0\)

The values of \(x\) are

\(2x = 0\)

or \(x = 0\)

and

\(2x-\frac{3}{2}=0\)

\(2x=\frac{3}{2}\)

\(x=\frac{3}{4}\)

\(x=0.75\)

Clearly \(x=\frac{3}{4}\) or \(0.75\) is greater than \(x=0\)

Therefore, the greatest value of \(x \text{ is } \frac{3}{4} = 0.75\)
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