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Question Number 201931 by hardmath last updated on 15/Dec/23

$$\mathrm{if}{(\mathrm{a}-2)}^2=4\mathrm{a}$$$$\mathrm{find}:5\mathrm{a}+4+\frac{16}{5\mathrm{a}+4}=?$$

Answered by mr W last updated on 16/Dec/23

$$a^2-4a+4=4a$$$$a^2-8a+4=0$$$${(a-4)}^2=12$$$$a=4\pm 2\sqrt{3}$$$$5a+4=24\pm 10\sqrt{3}$$$$\frac{16}{5a+4}=\frac{16}{24\pm 10\sqrt{3}}=96\mp 40\sqrt{3})$$$$5a+4+\frac{16}{5a+4}=24\pm 10\sqrt{3}+96\mp 40\sqrt{3})$$$$=30(4\pm \sqrt{3})$$

Commented by hardmath last updated on 16/Dec/23

$$\mathrm{cool}\mathrm{dear}\mathrm{professor}\mathrm{thankyou}$$

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