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Category: Arithmetic

if-x-x-1-x-1-are-first-three-terms-of-an-AP-then-what-is-the-sum-of-it-s-first-10-terms-equal-to-

Question Number 91912 by jagoll last updated on 03/May/20 $$\mathrm{if}\:\mid\mathrm{x}\mid,\:\mid\mathrm{x}−\mathrm{1}\mid,\:\mid\mathrm{x}+\mathrm{1}\mid\:\mathrm{are}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{AP}.\:\mathrm{then}\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{it}'\mathrm{s}\:\mathrm{first} \\ $$$$\mathrm{10}\:\mathrm{terms}\:\mathrm{equal}\:\mathrm{to}\: \\ $$ Commented by jagoll last updated on 03/May/20…

q-a-a-9-1-108-a-3-1-3-1-3-b-b-9-1-108-b-3-1-3-1-3-a-9-37-72-b-9-37-72-find-q-correct-to-5-decimal-places-

Question Number 157046 by ajfour last updated on 18/Oct/21 $${q}=\left\{{a}+\left(\frac{{a}}{\mathrm{9}}−\frac{\mathrm{1}}{\mathrm{108}}−{a}^{\mathrm{3}} \right)^{\mathrm{1}/\mathrm{3}} \right\}^{\mathrm{1}/\mathrm{3}} \\ $$$$\:\:+\left\{{b}+\left(\frac{{b}}{\mathrm{9}}−\frac{\mathrm{1}}{\mathrm{108}}−{b}^{\mathrm{3}} \right)^{\mathrm{1}/\mathrm{3}} \right\}^{\mathrm{1}/\mathrm{3}} \\ $$$$\:\:\:{a}=\frac{\mathrm{9}+\sqrt{\mathrm{37}}}{\mathrm{72}}\:\:\:,\:\:{b}=\frac{\mathrm{9}−\sqrt{\mathrm{37}}}{\mathrm{72}} \\ $$$$\:{find}\:\boldsymbol{{q}}\:{correct}\:{to}\:\mathrm{5}\:{decimal} \\ $$$$\:{places}. \\ $$ Commented…

nswer-to-25929-by-binome-formula-1-x-n-m-k-0-k-n-m-C-n-m-k-x-k-the-coefficent-of-x-n-is-C-n-m-n-and-the-coefficient-of-x-m-is-C-n-m-m-but-we-have-for-p-lt-

Question Number 25954 by abdo imad last updated on 16/Dec/17 $${nswer}\:{to}\:\mathrm{25929}\:\:\:{by}\:{binome}\:{formula}\:\:\: \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}+{m}} \:\:=\sum_{{k}=\mathrm{0}} ^{{k}={n}+{m}} \:{C}_{{n}+{m}} ^{{k}} \:{x}^{{k}} \:\:\:\:{the}\:{coefficent}\:{of}\:{x}^{{n}} \:{is}\: \\ $$$${C}_{{n}+{m}} ^{{n}} \:{and}\:{the}\:{coefficient}\:{of}\:{x}^{{m}} \:\:{is}\:\:\:{C}_{{n}+{m}}…

Question-25738

Question Number 25738 by yesaditya22@gmail.com last updated on 13/Dec/17 Answered by mrW1 last updated on 13/Dec/17 $$\frac{{a}+{b}}{\:\sqrt{{ab}}}=\mathrm{6} \\ $$$$\frac{\frac{{a}}{{b}}+\mathrm{1}}{\:\sqrt{\frac{{a}}{{b}}}}=\mathrm{6} \\ $$$${let}\:{t}^{\mathrm{2}} =\frac{{a}}{{b}}\geqslant\mathrm{0} \\ $$$$\frac{{t}^{\mathrm{2}} +\mathrm{1}}{{t}}=\mathrm{6}…

Question-156676

Question Number 156676 by mathlove last updated on 14/Oct/21 Commented by MathSh last updated on 14/Oct/21 $$\frac{\mathrm{2}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{c}}\:=\:\mathrm{3}\:\Rightarrow\:\frac{\mathrm{21}}{\mathrm{3}}\:=\:\mathrm{7} \\ $$ Answered by som(math1967) last updated on…