The HCF and LCM of 2 numbers are Xand Y are respectively 3 and 105 if x+y= 36 then - Maths - Real Numbers

Question

The HCF and LCM of 2 numbers are Xand Y are respectively 3 and 105
if x+y= 36 then 1/x+1/y=?

Lovina Kansal · Accepted Answer

Dear student
HCF of two numbers x and y=3LCM of two numbers x and y=105and x+y=36   
(1)We know,HCF×LCM=Product of two numbers⇒3×105=xy⇒xy=315⇒x=315y     
(2)Put the value of x in (1), we get315y+y=36⇒315+y2-36y=0⇒y2-36y+315=0⇒y2-15y-21y+315=0⇒yy-15-21(y-15)=0⇒(y-21)(y-15)=0⇒y-21=0 or y-15=0⇒y=21 or y=15Case 1: When y=21 then x=31521=15Then, 1x+1y=115+121=21+15315=36315=435Case 2: When y=15  then x=31515=21Then, 1x+1y=121+115=15+21315=36315=435 
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The HCF and LCM of 2 numbers are Xand Y are respectively 3 and 105. if x+y= 36 then 1/x+1/y=?