Question

Please solve this ??

Answer 1

GIVEN

$a-b=4\\a^2+b^2=40$

TO FIND

$ab\\a^3-b^3$

SOLUTION

We know,

$(a-b)^2 = a^2+b^2-2ab\\(4)^2=40-2ab\\16 = 40-2ab\\2ab = 24\\ab=12$

We also know,

$a^3-b^3 = (a-b)(a^2+b^2+ab) \\= (4)(40+12)\\=(4)(52)\\=208$

ANSWER

$ab = 12\\a^3-b^3=208$

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