Question

Sum of squares of 2 numbers is 2754, HCF of the numbers is 9, LCM is 135, nos are?

Answer 1

According to the question the sum of squares of two numbers is 2754.

Let the two numbers be X and Y.

Therefore you can write X² + Y² equals to 2754.

Also it is given that the HCF and LCM of the two numbers are 9 and 135 respectively.

We know the formula that the product of two numbers is equal to the product of HCF and LCM of the same number.

i.e. X * Y = LCM * HCF

or, (X + Y)² = X² + 2XY + Y²

or, (X + Y)² = 2754 + 2*9*135 = 2754 + 2430 = 5184

or, X + Y = √5184 = 72.

Now, we know XY = 1215 or, X = 1215/Y

or, 1215/Y + Y = 72

or, 1215 + Y² = 72Y

or, Y² - 72Y + 1215 = 0

or, Y² - (45+27)Y + 1215 = 0

or, Y² - 45Y - 27Y + 1215 = 0

or, Y(Y - 45) - 27(Y - 45) = 0.

or, (Y - 45)(Y-27) = 0.

Therefore, the two numbers are 27 and 45.