Question

if ab=5 and a-b=4 the vailed valu (a3+b3)

Answer 1

Answer:

± 126

Step-by-step explanation:

( a - b ) ^2 = a ^2 - 2ab + b ^2

( 4 ) ^2 = ( a ^2 + b ^2 ) - 2ab

16 = ( a ^2 + b ^2 ) - 2 ( 5 )

16 = ( a ^2 + b ^2 ) - 10

26 = a ^2 + b ^2 ------ ( 1 )

26 + 2ab = a ^2 + b ^2 + 2ab

26 + 2 ( 5 ) = ( a + b ) ^2

26 + 10 = ( a + b ) ^2

36 = ( a + b ) ^2

±6 = a + b ---- ( 2 )

a^3 + b^3 = ( a + b ) ( a ^2 - ab + b ^2 )

Using ( 1 ) and ( 2 ),

a ^3 + b ^3 = ( ±6) [ ( a^2 + b^2) - ab]

a ^3 + b ^3 = ( ±6 ) ( 26 - 5 )

a ^3 + b ^3 = ±6 ( 21 )

a ^3 + b ^3 = ± 126