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the LCM of two numbers is 60. Their GCf is 6 and their difference is 18. What are the two numbers?

Sagot :

konrad509
[tex]LCM(x,y)=60\\ GCF(x,y)=6\\ x-y=18\\\\ LCM(x,y)=\dfrac{|x\cdot y|}{GCD(x,y)}\\ 60=\dfrac{|x\cdot y|}{6}\\ |x\cdot y|=360\\\\\\ |x\cdot y|=360\\ x-y=18\\\\ |x\cdot y|=360\\ x=18+y\\\\ |(18+y)\cdot y|=360\\ |18y+y^2|=360\\ 18y+y^2=360 \vee 18y+y^2=-360\\ y^2+18y+81=441 \vee y^2+18y+81=-279\\ (y+9)^2=441 \vee (y+9)^2=-279\\ y+9=\sqrt{441} \vee y+9=-\sqrt{441}\\ y=21-9 \vee y=-21-9\\ y=12 \vee y=-30\\\\ x-12=18 \vee x-(-30)=18\\ x=30 \vee x=-12\\\\ \boxed{x=30, y=12 \vee x=-12, y=-30}[/tex]
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