Question

the difference between two numbers is 18 and the hcf and the LCM of these numbers are 3 and 273. What is the sum of the squares of these two numbers?​

Answer 1

Answer:

let,the 2 numb=a , b

a-b=18

hcf=3

LCM=273

hcf×lcm=3×273=819=a×b

a=18+b

ab=819

(18+b)b=819

b^2+18b-819=0

solve this equation and u will get the answer...

Step-by-step explanation:

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Answer 2

Question :

The difference between two numbers is 18 and the hcf and the LCM of these numbers are 3 and 273. What is the sum of the squares of these two numbers?

Theory :

If a and b are two positive integers

$\sf \: hcf \times lcm = a \times b$

Solution :

Given :

• Difference between two numbers is 18
• HCF and LCM of these numbers are 3 and 273

Let the two numbers be x and y .

According to the question:

$\sf \: x - y = 18...(1)$

HCF = 3 and LCM =273

$\sf \: hcf \times lcm = xy$

$\sf \implies3 \times 273 = xy$

$\sf \implies \: xy = 819...(2)$

We have to find the sum of the squares of these two numbers.

$\sf (x - y) {}^{2} = x {}^{2} + y {}^{2} - 2xy$

$\sf \implies \: x {}^{2} + y {}^{2} = (x - y) {}^{2} + 2 xy$

Now put the values of equation (1) and (2)

$\sf \implies \: x {}^{2} + y {}^{2} = (18) {}^{2} + 2 \times 819$

$\sf \implies \: x {}^{2} + y {}^{2} = 324 + 1638 = 1962$