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If a+b=2 and a^2+b^2=6 show that ab=-1?

0 votes
Given that a+b = 2
and (a^2) + (b^2) = 6
Show that ab=-1
This is really simple, But I can't get it
asked Apr 12, 2013 in ALGEBRA 2 by homeworkhelp Mentor

1 Answer

+1 vote

a + b = 2 and a2 + b2 = 6

(a + b)2 = a2 + b2 + 2ab

Substitute a + b = 2 and a2 + b2 = 6 then

22 = 6 + 2ab

4 = 6 + 2ab

Subtract 4 from each side

0 = 6 - 4 + 2ab

0 = 2 + 2ab

Subtract 2 from each side

-2 = -2 + 2 + 2ab

-2 = 0 + 2ab

-2 = 2ab

Recall : Symetric property a = b then b = a

2ab = -2

Divide each side by 2

ab = -1.

answered Apr 12, 2013 by diane Scholar

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