<li>If a is 4 greater than b and a^2 + b^2 = 10, what is the value of ab?</li>
</ol>
<p>(A) 13
(B) 6
(C) 3
(D) -3
(E) -6</p>
<p>easy..</p>
<p>a = b+4
a^2 + b^2 = 10</p>
<p>(a-b)^2 = 4^2
a^2 - 2ab +b^2 = 16
10 -2ab = 16
-2ab = 6
ab = -3
~D~</p>
<p>can someone please explain it more clearly.</p>
<p>How did you get from the second line to the third line? I understand the rest...</p>
<p>Oh i get it. You subtracted b and squared both sides.</p>
<p>i would have done it this way...
a=b+4
a^2+b^2=10
substitute "b+4" for a so you get
(b+4)^2 +b^2=10
b^2 +8b+16+b^2=10
2b^2 +8b+6=0, divide everything by 2
b^2 +4b+3=0, so you get:
(b+1)(b+3)=0
b=-1, b=-3</p>
<p>back to a=b+4
1.) a=(-1)+4=3
2.) a=(-3)+4=-1</p>
<p>1.) ab=(3)(-1)=-3
2.) ab=(-3)(1)=-3</p>
<p>answer is D
hope this helps :)</p>
<p>This would be a good problem to plug into the calculator (ti-89 if you have one) to save at least a minute or two of time</p>