<ol>
<li>(a+b)2 less than equal to (a-b)2+36.</li>
</ol>
<p>In the equation above, 0less than eq to a and a is less than eq to b. what is the greatest possible value of a?</p>
<p>Is the (a+b)2 and the (a-b)2 referring to 2(a+b) or (a+b) squared?</p>
<p>*Side note: it is “less than or equal to”.</p>
<p>the greatest value is 3</p>
<p>greatest value is 9.</p>
<p>The greatest value is 9. After you foil out both sides of the inequality and simplify, you end up with 4ab < 36. Therefore ab must be < 9, making nine the greatest answer a can be if the answers must be integers.</p>
<p>Where are these problems from?</p>
<p>The greatest value is 3 since ab<=9 and since a<=b.</p>
<p>^I cannot believe I forgot to account for the fact that a<=b. 3 is the correct answer.</p>
<p>if it is (a+b)^2 then the max value is 3.</p>
<p>if it is 2(a+b) the the max value is 9.</p>
<p>alright how did you get that… i could care about the right answer since i already have it.</p>
<p>^what is the right answer??? At least tell us, so that we know what to explain.</p>
<p>my apologies, it is 3</p>
<p>(a+b)^2 <= (a-b)^2 +36</p>
<p>a^2 +2ab+b^2 <= a^2 -2ab+b^2 +36</p>
<p>4ab <= 36</p>
<p>ab <= 9</p>
<p>max value for a is 3.</p>
<p>wow i can’t believe i didn’t see that…thanks alot.</p>