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Category: Algebra

25-x-8-5-x-16-

Question Number 223685 by fantastic last updated on 02/Aug/25 $$\mathrm{25}^{{x}} −\mathrm{8}.\mathrm{5}^{{x}} =−\mathrm{16} \\ $$ Answered by Rasheed.Sindhi last updated on 02/Aug/25 $$\left(\mathrm{5}^{{x}} \right)^{\mathrm{2}} −\mathrm{8}\left(\mathrm{5}^{{x}} \right)=−\mathrm{16}…

Question-223703

Question Number 223703 by Rojarani last updated on 02/Aug/25 Answered by Rasheed.Sindhi last updated on 02/Aug/25 $$\left(\frac{{x}−\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{3}} =\frac{\mathrm{4}}{\mathrm{9}}+\sqrt[{\mathrm{4}}]{\frac{\mathrm{3}}{\mathrm{27}}}\:+\sqrt[{\mathrm{3}}]{\frac{\mathrm{9}}{\mathrm{27}}}\: \\ $$$$\frac{{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{1}}{\mathrm{27}}=\frac{\mathrm{4}}{\mathrm{9}}+\frac{\sqrt[{\mathrm{3}}]{\mathrm{3}}}{\mathrm{3}}\:+\frac{\sqrt[{\mathrm{3}}]{\mathrm{9}}}{\mathrm{3}}\: \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}}…

40-x-1-2-2x-1-

Question Number 223615 by fantastic last updated on 31/Jul/25 $$\mathrm{40}^{{x}−\mathrm{1}} =\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} \\ $$ Answered by mr W last updated on 31/Jul/25 $$\frac{\mathrm{40}^{{x}} }{\mathrm{40}}=\mathrm{2}×\mathrm{2}^{\mathrm{2}{x}} =\mathrm{2}×\mathrm{4}^{{x}} \\…

Question-223585

Question Number 223585 by hardmath last updated on 30/Jul/25 Commented by hardmath last updated on 30/Jul/25 $$\mathrm{Radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:=\:\mathrm{R} \\ $$$$\mathrm{AB}\:\bot\:\mathrm{CD} \\ $$$$\mathrm{AC}\:=\:\mathrm{a} \\ $$$$\mathrm{BD}\:=\:\mathrm{b} \\ $$$$\mathrm{Prove}\:\mathrm{that}:\:\mathrm{R}\:=\:\frac{\sqrt{\mathrm{a}^{\mathrm{2}}…

S-1-1-1-2-2-3-3-16-16-S-2-1-1-2-2-3-3-14-14-Find-S-1-S-2-

Question Number 223571 by hardmath last updated on 30/Jul/25 $$\mathrm{S}_{\mathrm{1}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+…+\:\mathrm{16}\centerdot\mathrm{16}! \\ $$$$\mathrm{S}_{\mathrm{2}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+…+\:\mathrm{14}\centerdot\mathrm{14}! \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{S}_{\mathrm{1}} }{\mathrm{S}_{\mathrm{2}} }\:=\:? \\ $$ Answered by parthasc last updated…