Question

If a – b = 5 and ab = 24 then the value of a + b is

Answer 1

hope this helps you.....

Answer 2

GIVEN:-

• if a - b = 5 and ab = 24.

TO FIND:-

• The Value of a + b

IDENTITIES USED :-

• $\rm{ (a+b)^2 = a^2 +b^2 + 2ab}$

• $\rm{ (a-b)^2 = a^2 -2ab + b^2 }$.

Now,

$\implies\rm{(a-b)^2 = a^2 +b^2 -2ab}$

$\implies\rm{ (5)^2 = a^2 + b^2 - 48}$

$\implies\rm{ 25 +48 = a^2 + b^2 }$

$\implies\rm{ 73 = a^2 +b^2}$

Therefore,

$\implies\rm{ (a+b)^2 = a^2 + b^2 + 2ab}$

$\implies\rm{ (a+b)^2 = 73 + 2\times{24}}$

$\implies\rm{ (a+b)^2 = 73 + 48}$

$\implies\rm{ (a+b)^2 = 121}$

$\implies\rm{ \sqrt{(a+b)} = \sqrt{121}}$

$\implies\rm{ a + b = 11.}$.

Hence, The Value of a + b is 11.