Question

a-b=7 ,ab=9 ,a×a-b×b

Answer 1

Given :- a - b = 7

ab :- 9

To find :- a² - b²

Solution :-

Using identity :- ( a - b )² :- a² + b² - 2ab

( 7 )² = a² + b² - 2 × 9

49 = a² + b² - 18

49 - 18 = a² + b²

31 = a² + b²

Now,

Using identity ( a + b )² = a² + b² + 2ab

( a + b )² = 31 + 2 × 9

( a + b )² = 31 + 18

( a + b )² = 49

a + b = √49

a + b = 7

a² - b ² = ( a + b ) ( a - b )

a² - b² = 7 × 7

a² - b² = 49