Question

if a+b=4 and ab=-12,find i) a+b ii) a^2-b^2​

Answer 1

Answer:

Step-by-step explanation:

Given, a+b = 4 ; ab = 12

(i) thus, a + b = 4

Squaring both sides,

(a+b ) ^2 = (4) ^ 2

=> a2 + b2 + 2ab = 16

Substituting values of ab

=> a2 + b2 + 2(12) = 16

=> a2 + b2 = 16 - 24

=> a2 + b2 = -6

From (i), we get,

a2 + b2 = -6

=> (a - b)2 + 2ab = -6

=> (a-b)2 = 6 - 24

=> (a-b) 2 = -18

=> (a-b) = root over -18

(ii) thus a^ 2 - b^ 2 = (a+b)(a-b)

                              = 4 * root over -18

                              = - 4 root 18

Ans: (i) a + b = 4 ; a^2 - b^2 = -4 root 18