If $u+v=7$ and $u^{2}+v^{2}=27$, what is the value... | Free GMAT Practice Question | GMAT Panda

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If u + v = 7 and u^{2} + v^{2} = 27, 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
$We substitute the known values (u + v)^{2} = 7^{2} = 49 and u^{2} + v^{2} = 27 into the expansion.$	$49 = 27 + 2 uv$	Theory & Tactics Method Card EQUA3-A Click to view full details
$We isolate the term uv by subtracting 27 from both sides.$	$49 - 27 = 2 uv$
$We solve for uv by dividing both sides by 2.$	$\frac{49 - 27}{2} = uv$

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A

If u + v = 7 and u^{2} + v^{2} = 27, 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
$We substitute the known values (u + v)^{2} = 7^{2} = 49 and u^{2} + v^{2} = 27 into the expansion.$	$49 = 27 + 2 uv$	Theory & Tactics Method Card EQUA3-A Click to view full details
$We isolate the term uv by subtracting 27 from both sides.$	$49 - 27 = 2 uv$
$We solve for uv by dividing both sides by 2.$	$\frac{49 - 27}{2} = uv$

Scroll horizontally to view all columns

A