Question

6. If H.C.F and L.C.M of two terms x and y are a and b respectively and x+y=a+b then x2 + y2 = ?​

Answer 1

Answer:

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Answer 2

Given:

H.C.F and L.C.M of two terms x and y are a and b

x+y=a+b

To find:

x²+y²

Solution:

The value of x²+y² is a²+b².

We can find the value by following the process given below-

We know that the value can be obtained by taking the square of x+y.

We also know that the product of LCM and HCF of two terms is equal to the product of the terms.

The product of HCF and LCM of x and y= The product of x and y

HCF×LCM=x×y

HCF of x and y=a

LCM of x and y=b

On putting the values, we get

a×b=x×y

ab=xy

Now, we have x+y=a+b.

Using the identity of (x+y)², we can find the value of x²+y².

On taking the square of x+y, we get

(x+y)²= x²+y²+2xy

On substituting the values of x+y and xy, we get

(a+b)²=x²+y²+2×ab

a²+b²+2ab= x²+y²+2ab

a²+b²=x²+y²

It is equal to the square of HCF and LCM of x and y.

Therefore, the value of x²+y² is a²+b².