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if-a-2-2-4a-find-5a-4-16-5a-4-




Question Number 201931 by hardmath last updated on 15/Dec/23
if   (a−2)^2  = 4a  find:   5a + 4 + ((16)/(5a + 4)) = ?
$$\mathrm{if}\:\:\:\left(\mathrm{a}−\mathrm{2}\right)^{\mathrm{2}} \:=\:\mathrm{4a} \\ $$$$\mathrm{find}:\:\:\:\mathrm{5a}\:+\:\mathrm{4}\:+\:\frac{\mathrm{16}}{\mathrm{5a}\:+\:\mathrm{4}}\:=\:? \\ $$
Answered by mr W last updated on 16/Dec/23
a^2 −4a+4=4a  a^2 −8a+4=0  (a−4)^2 =12  a=4±2(√3)  5a+4=24±10(√3)  ((16)/(5a+4))=((16)/(24±10(√3)))=96∓40(√3))  5a+4+((16)/(5a+4))=24±10(√3)+96∓40(√3))                             =30(4±(√3))
$${a}^{\mathrm{2}} −\mathrm{4}{a}+\mathrm{4}=\mathrm{4}{a} \\ $$$${a}^{\mathrm{2}} −\mathrm{8}{a}+\mathrm{4}=\mathrm{0} \\ $$$$\left({a}−\mathrm{4}\right)^{\mathrm{2}} =\mathrm{12} \\ $$$${a}=\mathrm{4}\pm\mathrm{2}\sqrt{\mathrm{3}} \\ $$$$\mathrm{5}{a}+\mathrm{4}=\mathrm{24}\pm\mathrm{10}\sqrt{\mathrm{3}} \\ $$$$\left.\frac{\mathrm{16}}{\mathrm{5}{a}+\mathrm{4}}=\frac{\mathrm{16}}{\mathrm{24}\pm\mathrm{10}\sqrt{\mathrm{3}}}=\mathrm{96}\mp\mathrm{40}\sqrt{\mathrm{3}}\right) \\ $$$$\left.\mathrm{5}{a}+\mathrm{4}+\frac{\mathrm{16}}{\mathrm{5}{a}+\mathrm{4}}=\mathrm{24}\pm\mathrm{10}\sqrt{\mathrm{3}}+\mathrm{96}\mp\mathrm{40}\sqrt{\mathrm{3}}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{30}\left(\mathrm{4}\pm\sqrt{\mathrm{3}}\right) \\ $$
Commented by hardmath last updated on 16/Dec/23
cool dear professor thankyou
$$\mathrm{cool}\:\mathrm{dear}\:\mathrm{professor}\:\mathrm{thankyou} \\ $$

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