Question Number 147894 by mathdanisur last updated on 24/Jul/21
$${x}^{\mathrm{2}} \:-\:\mathrm{3}{x}\:+\:\mathrm{4}\:=\:\mathrm{0}\:\:\Rightarrow\:\:{x}^{\mathrm{2}} \:+\:\frac{\mathrm{16}}{{x}^{\mathrm{2}} }\:=\:? \\ $$
Answered by mindispower last updated on 24/Jul/21
$$\Leftrightarrow{x}+\frac{\mathrm{4}}{{x}}=\mathrm{3} \\ $$$$\Rightarrow{x}^{\mathrm{2}} +\frac{\mathrm{16}}{{x}^{\mathrm{2}} }+\mathrm{8}=\mathrm{9} \\ $$
Commented by mathdanisur last updated on 24/Jul/21
$${Thankyou}\:{Sir} \\ $$
Answered by puissant last updated on 24/Jul/21
$$\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{4}=\mathrm{0}\:\Rightarrow\:\mathrm{x}^{\mathrm{2}} +\mathrm{4}=\mathrm{3x} \\ $$$$\Rightarrow\mathrm{x}+\frac{\mathrm{4}}{\mathrm{x}}=\mathrm{3} \\ $$$$\Rightarrow\left(\mathrm{x}+\frac{\mathrm{4}}{\mathrm{x}}\right)^{\mathrm{2}} =\mathrm{9} \\ $$$$\Rightarrow\mathrm{x}^{\mathrm{2}} +\mathrm{2x}\frac{\mathrm{4}}{\mathrm{x}}+\frac{\mathrm{16}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{9} \\ $$$$\Rightarrow\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{16}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{9}−\mathrm{8}=\mathrm{1}.... \\ $$
Commented by mathdanisur last updated on 24/Jul/21
$${Thankyou}\:{Sir} \\ $$