Question

(a-b)=2 and ab=24 then value of (a^2+b^2 ) ( a^3-b^3)​

Answer 1

Answer:

$a - b = 2 \\ a = 2 + b \\ \\ ab = 24 \\ (2 + b)b = 24 \\ 2b + {b}^{2} = 24 \\ {b}^{2} +2b - 24 = 0 \\ {b}^{2} + 6b - 4b - 24 = 0 \\ b(b + 6) - 4(b + 6) = 0 \\ (b + 6)(b - 4) = 0 \\ b + 6 = 0 \: \: \: or \: \: \: b - 4 = 0 \\ \boxed{ \large b = \underline{ \underline{ \bf - 6}} \: \: \: or \: \: \: b = \underline{ \underline{ \bf 4}}} \\ \\ a - b = 2 \\ a - 4 = 2 \\ a = 2 + 4 \\ \boxed{ \large a = \underline{ \underline{ \bf 6}}} \\ \\ \large a ={ \bf 6}, \: \: \large b ={ \bf 4} \\ \\ ( {a}^{2} + {b}^{2} )( {a}^{3} - {b}^{3} ) \\ = ( {6}^{2} + {4}^{2} )( {6}^{3} - {4}^{3} ) \\ = (36 + 16)(216 - 64) \\ = 52 \times 152 \\ \boxed{ \large = \underline{ \underline{ \bf 7904}}}$