The l. c.m and h. c.f of two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find the HCF of two numbers.

50

Step-by-step explanation:

There are 2 prime factors that are different and 2 numbers that we look for that are identical when looking for prime factors.

So  for numbers that don't end in 0 like 500 we can start with 3 to get 27 as one of the two numbers, then we look to see if 27 divides into that.

But for 500 it will always be numbers that end in  0 or 5  and also 1,  2 and 4

So we work with 9+1 = 10

x = 10

500/10 = 50

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8