Question

if a+b=-5 ab=-14 find
${a}^{3} - {b}^{3}$

Answer 1

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Answer 2

$\huge{\underline{\underline{\red{♡Solution→}}}}$

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$\bold{\huge{\underline{\underline{\rm{ Given :}}}}}$

$a + b = - 5 \\ ab = - 14$

$\bold{\huge{\underline{\underline{\rm{ To\:Find :}}}}}$

${a}^{3} - {b}^{3} = ?$

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$\purple{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

We know that →

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

So,

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

${a}^{2} + {b}^{2} = ( { - 5)}^{2} - 2 \times ( - 14) \\ {a}^{2} + {b}^{2} = 25 + 28 \\ {a}^{2} + {b}^{2} = 53$

Now , there is one more formula ,

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

So,

$( {a - b)}^{2} = 53 - 2 \times ( - 14) \\ a - b = \sqrt{53 + 28} \\ a - b = \sqrt{81} \\ a - b = 9$

The formula of a³ - b³ is →

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

Now put the values that we have figure out →

${a}^{3} - {b}^{3} = (9)(53 </strong><strong>+</strong><strong> ( - 14)) \\ {a}^{3} - {b}^{3} = 9(53 </strong><strong>-</strong><strong> 14) \\ {a}^{3} - {b}^{3} = 9 \times </strong><strong>3</strong><strong>9</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>x</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong> {a}^{3} - {b}^{3} = \: </strong><strong>3</strong><strong>5</strong><strong>1</strong><strong>}</strong><strong>}</strong><strong>$

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