Question

a3+b3=19 a+b=1 what is the value of ab
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Answer 1

Answer:

a³+b³ = (a+b)³-3ab(a+b) ==> 19 = 1-3ab ; 3ab = -18, ab = -6.

Answer 2

Answer:

ab = -6

Step-by-step explanation:

given:

${a}^{3} + {b}^{3} = 19$

$a+b=1$

To find $ab$,

we know that,

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

therefore,

$(a + b)( {a}^{2} - ab + {b}^{2} ) = 19$

its given that $a+b=1$

=> $(1)( {a}^{2} + {b}^{2} - ab) = 19$

we know that ${a}^{2} + {b}^{2}$ can also be written as,

${a}^{2} + {b}^{2} + 2ab - 2ab$

= ${(a + b)}^{2} - 2ab$

therefore,

=> ${(a + b)}^{2} - 2ab - ab = 19$

=> ${(1)}^{2} - 3ab = 19$

=> $1 - 3ab = 19$

=> $-3ab = 19+1$

=> $3ab = -18$

=> $ab = \frac{ - 18}{3}$

=> $ab = -6$

hence, ab = -6