Question

Find x cube - y cube If, x-y=11,xy=2
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Answer 1

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Your Answer is Below

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Given:-

x - y = 11

xy = 2

To Find:-

$x^{3} - y^{3}$

Formula Using:-

• $(x-y)^{3} =x^{3}-y^{3} -\ 3x^{2} y\ +\ 3xy^{2}$

Explanation:-

x - y = 11

Taking cube on both sides , we get

⇒ $(x-y)^{3} = 11^{3}$

⇒ $x^{3} -y^{3} -3x^{2} y\ +3xy^{2} = 1331$

⇒ $x^{3} -y^{3} -3xy ( x - y ) = 1331$

substituting value of ( x - y = 11 ) in equation. we get,

⇒ $x^{3} -y^{3} -3xy ( 11 ) = 1331$

now substituting value of ( xy = 2 ) in equation. we get,

⇒ $x^{3} -y^{3} -3(2 ) ( 11 ) = 1331$

⇒ $x^{3} -y^{3} -6(11) = 1331$

⇒ $x^{3} -y^{3} -66 = 1331$

⇒ $x^{3} -y^{3} = 1331 + 66$

⇒ $x^{3} -y^{3} = 1397$

                              $\huge{\ornage{\boxed{\boxed{\pink{\green{\mathscr{ x^{3} -y^{3}=1397 }}} }} }}}$

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Hope It Helps You Dear ! :D     ^_^

By Abhiram5566

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