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If a² - 2ab + b² = 36 and a² - 3ab + b² = 22 the ab = ____?
If a² - 2ab + b² = 36 and a² - 3ab + b² = 22 the ab = ____?
8
6
14
None of these
Explanation
The given equations can be rewritten using identity formulas:
a² - 2ab + b² = (a - b)² = 36 → (a - b) = ±6
a² - 3ab + b² = 22 → (a - b)² - ab = 22
Substituting
(a - b)² = 36
in
36 - ab = 22
, solving for
ab
gives:
a
b
=
36
−
22
=
14