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Question Number 190115 by HeferH last updated on 27/Mar/23

$$\mathrm{if}:(\mathrm{a}+\mathrm{b})(\mathrm{a}+1)=\mathrm{b}$$$$\mathrm{find}:\mathrm{P}=\sqrt{{\mathrm{a}}^3+{\mathrm{b}}^3-3\mathrm{ab}}$$

Answered by som(math1967) last updated on 27/Mar/23

$$(a+b)(a+1)=b$$$$\Rightarrow a^2+a+ab+b=b$$$$\Rightarrow a(a+b+1)=0$$$$ifa=0$$$$thenP=\sqrt{b^3}=b^{\frac{2}{3}}$$$$ifa+b+1=0$$$$(a+b)=-1$$$$\Rightarrow {(a+b)}^3=-1$$$$a^3+b^3+3ab(a+b)=-1$$$$\Rightarrow a^3+b^3-3ab=-1$$$$\Rightarrow \sqrt{a^3+b^3-3ab}=\sqrt{-1}$$$$\therefore P=i$$

Commented by HeferH last updated on 27/Mar/23

$$\mathrm{Thanks}!$$

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