The number 63-36 sqrt(3) can be expressed as x+y sqrt(3) for some integers x and...

Question

The number 63-36 sqrt(3) can be expressed as x+y sqrt(3) for some integers x and y. What is the value of x y ?

GMAT Panda · Accepted Answer

-18 We let integers x and y satisfy the given form. 63 - 36 sqrt(3) = x + y sqrt(3) We square both sides and expand the result. 63 - 36 sqrt(3) = x^2 + 3y^2 + 2xy sqrt(3) We separate the equation into its rational part and its irrational part. x^2 + 3y^2 = 63 2xy = -36 We solve the second equation for the product of x and y. xy = -18

Explanation	Calculations	Help
$We let integers x and y satisfy the given form.$	$63 - 363 = x + y 3$
$We square both sides and expand the result.$	$63 - 363 = x^{2} + 3 y^{2} + 2 x y 3$
$We separate the equation into its rational part and its irrational part.$	$x^{2} + 3 y^{2} = 63 2 x y = - 36$
$We solve the second equation for the product of x and y.$	$x y = - 18$

Question

Options:

Steps

Final Answer

Question

Options:

Steps

Final Answer

Related questions