Question

If a(2-√3)=b(2+√3)=1 then find the value of a square minus b square is equal to what

Answer 1

Answer:

8 √3

Step-by-step explanation:

Given----> a ( 2 - √3 ) = b ( 2 + √3 ) = 1

To find-----> Value of ( a² - b² ) .

Solution----> ATQ,

a ( 2 - √3 ) = b ( 2 + √3 ) = 1

So , a ( 2 - √3 ) = 1

Multiplying both sides by ( 2 + √3 ) , we get,

=> a ( 2 - √3 ) ( 2 + √3 ) = 1 ( 2 + √3 )

=> a { ( 2 )² - ( √3 )² } = ( 2 + √3 )

=> a ( 4 - 3 ) = ( 2 + √3 )

=> a ( 1 ) = ( 2 + √3 )

=> a = ( 2 + √3 )

Similarly , b = ( 2 - √3 )

Now, a² = ( 2 + √3 )²

We know that ,

( a + b )² = a² + b² + 2ab , applying it , we get,

= ( 2 )² + ( √3 )² + 2 ( 2 ) ( √3 )

= 4 + 3 + 4 √3

= 7 + 4√3

b² = ( 2 - √3 )²

( a - b )² = a² + b² - 2ab

= ( 2 )² + ( √3 )² - 2 ( 2 ) ( √3 )

= 4 + 3 - 4 √3

= 7 - 4√3

a² - b² = ( 7 + 4√3 ) - ( 7 - 4√3 )

a² - b² = 7 + 4√3 - 7 + 4√3

= 8 √3

Answer 2

Answer:

if a=3 and b=-1, then the value of is (a+b) b is