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Question Number 10102 by konen last updated on 23/Jan/17

$$\mathrm{a}-\mathrm{b}=\frac{\mathrm{a}+\mathrm{b}}{7}=\frac{\mathrm{a}\times \mathrm{b}}{24}\Rightarrow \mathrm{a}-\mathrm{b}=?$$

Answered by mrW1 last updated on 23/Jan/17

$$\mathrm{a}-\mathrm{b}=\frac{\mathrm{a}+\mathrm{b}}{7}=\frac{\mathrm{a}\times \mathrm{b}}{24}=u$$$$a-b=u$$$$a+b=7u$$$$a\times b=24u$$$${(a+b)}^2-{(a-b)}^2={\left(7u\right)}^2-u^2=48u^2$$$$4\times a\times b=48u^2$$$$4\times 24u=48u^2$$$$u^2-2u=0$$$$u(u-2)=0$$$$\Rightarrow u=0or2$$$$i.e.a-b=0or2$$

Answered by arge last updated on 24/Jan/17

$$7(a-b)=a+b$$$$24(a-b)=ab$$$$$$$$a=7(a-b)-b$$$$$$$$a=\frac{24(a-b)}{b}$$$$$$$$7a-7b-b=\frac{24(a-b)}{b}$$$$$$$$7ab-8b^{2^{}}=24a-24b$$$$7ab-24a=8b^2-24b$$$$a(7b-24)=8b^2-24b$$$$$$$$a=\frac{8b^2-24b}{(7b-24)}$$$$$$$$\frac{ab}{24}=a-b$$$$ab=24a-24b$$$$$$$$\frac{8b^{3^{}}-24b^2}{7b-24}=\frac{192b^2-576b}{7b-24}-24b$$$$$$$$\frac{8b^3-24b^2}{7b-24}=\frac{192b^2-576b-168b^2+576}{7b-24}$$$$$$$$8b^3-24b^2=24b^2$$$$8b^3-48b^2=0$$$$b^3-6b^2=0$$$$b^2(b-6)=0$$$$$$$$b=0yb=6$$$$$$$$a=indcuandoa=0$$$$a=8cuandoa=6$$$$$$$$a-b=2\ast \ast \ast Rta$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

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