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Question
If a - b = 7 and ab = 18; find a + b.
Solution
We know that,
( a - b )2 = a2 - 2ab + b2
and
( a + b )2 = a2 + 2ab + b2
Rewrite the above equation, we have
( a + b )2 = a2 + b2 - 2ab + 4ab
= ( a + b )2 + 4ab ...(1)
Given that a - b = 7; ab = 18
Substitute the values of ( a - b ) and (ab)
in equation (1), we have
( a + b )2 = (7)2 + 4(18)
= 49 + 72 = 121
⇒ a + b = `+- sqrt121`
⇒ a + b = `+-11`
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