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