Question

if a^2- b^2= 36 and a-b = 12 then average of 'a' and 'b' is ?
A) 3
B) 12
C) 6
D 3/2

Answer 1

a^2-b^2=36
(a+b)(a-b)=36
here a-b=12 so that
(a+b)(12)=36
a+b=36÷12
a+b=3

Answer 2

Given a^2 - b^2 = 36 ------- (1)

Given a - b = 12 ------ (2)

Equation (1) can be written as:

= > (a + b)(a - b) = 36

= > (a + b)(12) = 36

= > (a + b) = 36/12

= > a + b = 3 -------- (3)

Now,

On solving (2) & (3), we get

= > a + b = 3

= > a - b = 12

---------------

2a = 15

a = 15/2.

Substitute a = (15/2) in (3), we get

= > a + b = 3

= > (15/2) + b = 3

= > b = 3 - (15/2)

= > b = 6 - 15/2

= > b = -9/2.

Now,

Average of a and b is:

$= > \frac{\frac{15}{2} - \frac{9}{2}}{2}$

$= > \frac{\frac{15 - 9}{2}}{2}$

$= > \frac{6}{4}$

$= > \boxed{\frac{3}{2}}}$

The answer is option - D.

Hope this helps!