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Question Number 7478 by Yozzia last updated on 31/Aug/16
Find the value of  x^3 (x^3 −18)  if  x(x−3)=−1.
$${Find}\:{the}\:{value}\:{of}\:\:{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{18}\right)\:\:{if}\:\:{x}\left({x}−\mathrm{3}\right)=−\mathrm{1}. \\ $$
Answered by Rasheed Soomro last updated on 31/Aug/16
   x^3 (x^3 −18)  if  x(x−3)=−1  [x(x−3)]^3 =(−1)^3   (a−b)^3 =a^3 −b^3 −3ab(a−b)  x^3 (x^3 −27−9x(x−3))=−1  x^3 (x^3 −27−9(−1)=−1  x^3 (x^3 −27+9)=−1   x^3 (x^3 −18)=−1
$$\:\:\:{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{18}\right)\:\:{if}\:\:{x}\left({x}−\mathrm{3}\right)=−\mathrm{1} \\ $$$$\left[{x}\left({x}−\mathrm{3}\right)\right]^{\mathrm{3}} =\left(−\mathrm{1}\right)^{\mathrm{3}} \\ $$$$\left({a}−{b}\right)^{\mathrm{3}} ={a}^{\mathrm{3}} −{b}^{\mathrm{3}} −\mathrm{3}{ab}\left({a}−{b}\right) \\ $$$${x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{27}−\mathrm{9}{x}\left({x}−\mathrm{3}\right)\right)=−\mathrm{1} \\ $$$${x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{27}−\mathrm{9}\left(−\mathrm{1}\right)=−\mathrm{1}\right. \\ $$$${x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{27}+\mathrm{9}\right)=−\mathrm{1} \\ $$$$\:{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} −\mathrm{18}\right)=−\mathrm{1} \\ $$

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