Question

If the sum of squares of two numbers is 2754 and their hcf and lcm are 9 and 135 respectively, then the numbers are

a.27, 36

b. 27, 35

c. 28, 45

d. 27, 45

Answer 1

Answer:

d.27&45

Step-by-step explanation:

let one no. be x

other no. be y

ATQ,

x^2+y^2=2754- - -1

HCF(x,y)=9

LCM(x,y)=135

since

HCF*LCM=product of two numbers

therefore

9*135=xy

xy=1215- - - 2

(x+y)^2=x^2+y^2+2xy

=2754+2(1215)[from 1&2]

=5184

therefore

x+y=√5184

x+y=72- - -3

from 2

y=1215/x

now,

on putting value of y in 3 ,we get

x+1215/x=72

x^2-72x+1215=0- - - 4

on solving 4

we get,

x^2-27x-45x+1215=0

(x-45)(x-27)=0

therefore

x=45,27

now,putting values of y in 3

if x=45

then y=27

if x=27

then y=45

therefore numbers are= 27 & 45