Question Number 217519 by Ari last updated on 15/Mar/25
Commented by Ari last updated on 15/Mar/25
$${Find}\:\:{x}\: \\ $$
Answered by mr W last updated on 15/Mar/25
$$\mathrm{39}^{\mathrm{2}} =\left(\mathrm{2}{a}\right)^{\mathrm{2}} +\mathrm{43}^{\mathrm{2}} −\mathrm{2}{a}×\mathrm{43} \\ $$$$\mathrm{2}{a}^{\mathrm{2}} −\mathrm{43}{a}+\mathrm{164}=\mathrm{0} \\ $$$$\Rightarrow{a}=\frac{\mathrm{43}+\sqrt{\mathrm{537}}}{\mathrm{4}} \\ $$$${x}=\sqrt{{a}^{\mathrm{2}} +\mathrm{43}^{\mathrm{2}} −\mathrm{43}{a}} \\ $$$$\:\:=\frac{\sqrt{\mathrm{12287}−\mathrm{43}\sqrt{\mathrm{537}}}}{\mathrm{2}\sqrt{\mathrm{2}}}\approx\mathrm{37}.\mathrm{57} \\ $$
Commented by Ari last updated on 15/Mar/25
$${thanks}\:{sir}! \\ $$