If $u+v=8$ and $u^{2}+v^{2}=50$, what is the value... | Free GMAT Practice Question | GMAT Panda

👋 Hi! I'm GMAT Panda. Ask me anything about this question, or click a button below to get started!

If u + v = 8 and u^{2} + v^{2} = 50, what is the value of uv ?

Explanation	Calculations	Help
$We apply the development formula for the square of a sum.$	$(u + v)^{2} = u^{2} + v^{2} + 2 uv$	Theory & Tactics Method Card ALG4-A Click to view full details
$We substitute the known values (u + v)^{2} = 8^{2} = 64 and u^{2} + v^{2} = 50 into the expansion.$	$64 = 50 + 2 uv$	Theory & Tactics Method Card EQUA3-A Click to view full details
$We isolate the term uv by subtracting 50 from both sides.$	$64 - 50 = 2 uv$
$We solve for uv by dividing both sides by 2.$	$\frac{64 - 50}{2} = uv$

Scroll horizontally to view all columns

C

If u + v = 8 and u^{2} + v^{2} = 50, what is the value of uv ?

Explanation	Calculations	Help
$We apply the development formula for the square of a sum.$	$(u + v)^{2} = u^{2} + v^{2} + 2 uv$	Theory & Tactics Method Card ALG4-A Click to view full details
$We substitute the known values (u + v)^{2} = 8^{2} = 64 and u^{2} + v^{2} = 50 into the expansion.$	$64 = 50 + 2 uv$	Theory & Tactics Method Card EQUA3-A Click to view full details
$We isolate the term uv by subtracting 50 from both sides.$	$64 - 50 = 2 uv$
$We solve for uv by dividing both sides by 2.$	$\frac{64 - 50}{2} = uv$

Scroll horizontally to view all columns

C