Question

If a+b=5 and a2+b2=13 then ab=

Answer 1

Given:

• a + b = 5

• a² + b² = 13

To find out:

Find the value of ab ?

Solution:

We know that,

( a + b )² = a² + b² + 2ab

Substituting the values in the above formula, we get

⇒ ( 5 )² = 13 + 2 ( ab )

⇒ 25 = 13 + 2 ( ab )

⇒ 25 - 13 = 2 ( ab )

⇒ 12 = -2 ( ab )

⇒ ab = 12/2

⇒ ab = 6

Some useful identities:

• ( a - b )² = a² + b² - 2ab

• ( a - b ) ( a + b ) = a² - b²

• ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

• ( a + b )³ = a³ + b³ + 3ab ( a + b )

IDENTITY : An identity is an equality which is true for all values of the variables.