Question

if l and m are two positive integers such that l>3m, l2+9m2=369 and lm=60
find l-3m/12

Answer 1

Answer: 14

Step-by-step explanation:

$(l+3m)^{2} = l^{2} + 9m^{2}+6lm$

$l+3m=\sqrt{369+6*60} = \sqrt{729} = 27$    Eq (1)

Similarly :

$(l-3m)^{2} = l^{2} + 9m^{2}-6lm$

$l-3m = \sqrt{369-6*60} = \sqrt{9} = 3$        Eq (2)

Now add Eq (1) and Eq (2)

$2*l=30\\l=15$

Subtract Eq (2) from Eq (1)

$6*m= 24\\m=4$

So,

$l-\frac{3m}{12} = 15-\frac{3*4}{12} = 15-1 = 14$