<p>Advanced Algebra</p>
<p>if <em>x</em> can be expressed as y^2, where y is a positive integer, then let <em>x</em>= y^3 / 2. For example, since 9= 3^2, <em>9</em>= 3^3 /2 = 27/2 = 13.5. </p>
<p>if <em>m</em>= 4, what is the value of <em>4m</em>?</p>
<hr>
<p>very lost here. explain step by step ?</p>
<p>Math geniuses, now is the time :D</p>
<p>Okay, here's the problem. You have y twice, in two places that don't work together (I was looking at this last night).</p>
<p>To say that <em>x</em> can be expressed as y^2 implies that <em>x</em>=y^2, but also equals y^3/2. That doesn't work because the example provided doesn't satisfy both of those equalities. How about this?</p>
<p>If x can be expressed as y^2, then <em>x</em>=y^3/2. This should make the question more reasonable.</p>
<p><em>m</em>=4
y^3/2=4 for some y
y=2 by solving.</p>
<p>So m=y^2=4, which means <em>4m</em>=<em>16</em></p>
<p>16=4^2, so <em>4m</em> = <em>16</em> = 4^3/2 = 64/2 = 32</p>
<p>Is that correct?</p>
<p>x can be expressed as y^2; thus, sqr(x) = +/- y, an integer; from this, x is a perfect square
<em>x</em> = y^3 / 2</p>
<p>Since x is simply a variable, you can replace it with any number or any other symbol</p>
<p><em>m</em> = 4
<em>m</em> = y^3 / 2 -> 4 = y^3 / 2 -> 8 = y^3 -> y = 8^(1/3) = 2</p>
<p>By definition, m is y^2, so m is also 4; so, 4m = 16</p>
<p>16 = y^2 -> y = 4
<em>16</em> = 4^3 / 2 = 64 / 2 = 32</p>
<p><em>4m</em> = 32</p>
<p>Another way:</p>
<p><em>y^2</em> = y^3 /2 <------- (A)</p>
<p>I.
<em>m</em> = 4 means
m=y^2 and y^3 /2 = 4</p>
<p>II.
4m = (4)y^2 = (2y)^2
<em>4m</em> = <em>(2y)^2</em>
<em>(2y)^2</em> = (2y)^3 /2
<em>(2y)^2</em> = (8)y^3 /2
<em>(2y)^2</em> = (8)4
<em>(2y)^2</em> = 32</p>
<h1><em>4m</em> = 32.</h1>
<p>To make part II more clear (but longer):
4m = (4)y^2 = (2y)^2
Let n=2y
4m = n^2 <----------- (B)
<em>4m</em> = <em>n^2</em>
<em>n^2</em> = n^3 /2 <------------ from (A)
<em>n^2</em> = (2y)^3 /2
<em>n^2</em> = (8)y^3 /2
<em>n^2</em> = (8)4
<em>n^2</em> = 32
<em>4m</em> = 32.</p>
<p>oh shoot,i wanted to answer,but already enough explanations</p>