<p>I got this question while doing a practice test and I actually didn't even understand what was being asked.</p>
<p>"For what positive number is the square root of the number the same as the number divided by 40?"</p>
<p>A second one was:</p>
<p>"If 0 < (or equal to) x < (or equal to) y and (x + y)2 - (x - y)2 > (or equal to) 25, what is the least possible value of y?</p>
<p>Both were grid-ins.</p>
<p>If anyone could explain it I would appreciate it.</p>
<p>Thanks a lot</p>
<p>1st problem:</p>
<p>square root (x) = x/40 - square both sides
x = x^2/1600 - Set equal to zero
0 = x^2/1600 - x + 0 - Solve using quadratic formula
(1 +/- squareroot (1 - 4<em>1/1600</em>0))/ (2/1600) - Simplify
(1 +/- 1)/ 1/800 - Cannot be the negative one since the answer must be a positive number
(1 + 1)/ (1/800) = 1600</p>
<p>2nd problem:</p>
<p>(x+y)^2 - (x-y)^2 > 25 - Expand left side
(x^2 + 2xy + y^2) (- x^2 + 2xy - y^2) > 25 - Combine terms on left side
4xy > 25 - Y will be at its lowest value when x is at its highest, and since x is less than or equal to y, x and y will be equal.
4y^2 > 25 - Divide out the 4
y^2 > 25/4 - Square root both sides
y > 5/2</p>
<p>thanks a lot!</p>
<p>x = x^2/1600</p>
<p>Just divide both sides by x (since you know x is positive), which immediately yields x = 1600.</p>