Question

if a minus b is equal to -1 comma ab mai is equal to - 12 find a cube minus b cube​

Answer 1

Answer

$\boxed{\textbf{\large{a cube - b cube = 35}}}$

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Explanation :

a - b = -1

ab = -12

a^3 - b^3 = ?

☑ we know,

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

☑ we already have the values of ( a -b)and ab , we have to find the value of (a^2 + b^2),using The identity ( a - b)^2 we can find the value of a^2 - b^2

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

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

( - 1 )^2 + 2 ( - 12 ) = (a^2 + b^2 )

1 - 24 = (a^2 + b^2 )

so, (a^2 + b^2 ) = -23

☑ verification of the value of

(a^2 + b^2 )

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

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

( 1 ) = ( - 23) - (2 (-12))

( 1 ) = ( -23 ) + 24

1 = 1

hence verified

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☑ Therefor,

a^3 - b^3

= ( a - b) ( a^2+ab+b^2 )substitute all the values in the formula

a^3 - b^3 = ( -1 ) ( (a^2 + b^2 ) + ab)

= (-1) ((-23)+(-12))

= ( - 1 ) ( -35 )

= 35

$\boxed{\textbf{\large{a cube - b cube = 35}}}$

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