Question

if a^2 + b^2 = 10 ; and a = 13 find:
1: (a-b)
2:(a+b)

Answer 1

In the above Question , the following values are given -

a² + b² = 100 and ab = 13

To find -

Find the value of -

1. ( a - b )

2. ( a + b )

Solution -

Here ,

a² + b² = 100 and ab = 13

Now , let us consider equation 1 , which is -

a² + b² = 100

Suppose that in the first case , we subtract 2ab from both sides .

So , the equation becomes -

a² + b² = 100

=> a² + b² - 2ab = 100 - 2ab

But , we know that, a² - 2ab + b² = ( a - b )²

So ,

=> ( a - b )² = 100 - 2ab

Now , ab = 13. So , 2ab = 26 .

100 - 2ab = 74

=> ( a - b )² = 74

=> ( a - b ) = √ 74 or { 74 }^½

Similarly -

Now , let us consider equation 1 , which is -

a² + b² = 100

Suppose that in the second case , we add 2ab from both sides .

So , the equation becomes -

a² + b² = 100

=> a² + b² + 2ab = 100 + 2ab

But , we know that, a² + 2ab + b² = ( a + b )²

So ,

=> ( a + b )² = 100 + 2ab

Now , ab = 13. So , 2ab = 26 .

100 + 2ab = 126

=> ( a + b )² = 74

=> ( a + b ) = √ 126 or { 126 }^½

This is the required answer .

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