Algebra – Page 824

Question-144820

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Question Number 144820 by mathdanisur last updated on 29/Jun/21 Answered by mathmax by abdo last updated on 30/Jun/21 $I = \int_{0}^{1} \frac{\log (1 + \sqrt{x (1 - x)})}{x (1 - x)} dx changement x = \sin^{2} t give$ $$\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…

Let-a-b-gt-0-and-a-b-1-3ab-Prove-that-a-1-b-1-b-1-a-1-a-b-

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Question Number 144823 by loveineq last updated on 29/Jun/21 $Let a, b > 0 and a + b + 1 = 3 a b . Prove that$ $\frac{a + 1}{b + 1} + \frac{b + 1}{a + 1} ⩽ a + b$ Answered by ArielVyny last updated on 30/Jun/21 $w e k n o w t h a t a + b + 1 = 3 a b$ $${we}\:{suppose}\:{ab}\geqslant\mathrm{1} \…

solve-x-3-7x-2-7-x-15-lt-0-

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Question Number 79279 by jagoll last updated on 24/Jan/20 $solve$ $∣ x ∣^{3} - {7 x}^{2} + 7 ∣ x ∣ + 15 < 0$ Commented by jagoll last updated on 24/Jan/20 $$\mathrm{thanks}\: \…

Prove-that-if-p-gt-q-gt-0-and-x-0-1-p-x-p-p-1-1-1-q-x-q-q-1-1-

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Question Number 13731 by prakash jain last updated on 22/May/17 $Prove that if p > q > 0 and x ⩾ 0$ $\frac{1}{p} (\frac{x^{p}}{p + 1} - 1) ⩾ \frac{1}{q} (\frac{x^{q}}{q + 1} - 1) .$ Commented by mrW1 last updated on 25/May/17 $${function}\:{f}\left({x}\right)=\frac{\mathrm{1}}{{x}}\left(\frac{{a}^{{x}}…

3s-2-2ps-3cp-1-0-and-3s-2p-sp-2-3cp-2-0-find-s-and-p-both-real-in-terms-of-c-R-

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Question Number 79256 by ajfour last updated on 23/Jan/20 $3 s^{2} - 2 p s - 3 c p - 1 = 0 a n d$ $3 s - 2 p - {s p}^{2} - 3 {c p}^{2} = 0$ $f i n d s a n d p b o t h r e a l i n t e r m s$ $o f c \in R .$ Answered by MJS last…

Question-79249

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Question Number 79249 by Pratah last updated on 23/Jan/20 Commented by mr W last updated on 23/Jan/20 $c a n y o u t e l l a c c o r d i n g t o t h e d e f i n i t i o n$ $i n y o u r q u e s t i o n$ $[0.8] = 0$ $$\left[−\mathrm{0}.\mathrm{8}\right]=?\:\: \…

x-3-x-c-0-let-x-t-p-t-q-t-p-t-p-t-q-t-q-3-t-p-t-q-3-t-q-t-p-t-p-t-q-c-0-let-t-q-3-t-p-1-0-4t-1-p-q-4t-4p-3p-q-1-4t-4q-1-p-3q-3p-q-1

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Question Number 144768 by ajfour last updated on 04/Jul/21 $x^{3} - x - c = 0$ $l e t x = \sqrt{t + p} + \sqrt{t + q}$ $(t + p) \sqrt{t + p} + (t + q) \sqrt{t + q}$ $+ 3 (t + p) \sqrt{t + q} + 3 (t + q) \sqrt{t + p}$ $- \sqrt{t + p} - \sqrt{t + q} - c = 0$ $l e t (t + q) + 3 (t + p) - 1 = 0$ $\Rightarrow 4 t = 1 - (p + q)$ $$\Rightarrow\:\:\mathrm{4}{t}+\mathrm{4}{p}=\mathrm{3}{p}−{q}+\mathrm{1}…

1-x-x-1-1-x-1-x-2-1-x-2-x-3-3-4-

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Question Number 79233 by jagoll last updated on 23/Jan/20 $\frac{1}{x (x + 1)} + \frac{1}{(x + 1) (x + 2)} +$ $\frac{1}{(x + 2) (x + 3)} ⩽ \frac{3}{4}$ Commented by john santu last updated on 23/Jan/20 $\frac{1}{x} - \frac{1}{x + 1} + \frac{1}{x + 1} - \frac{1}{x + 2}$ $$+\frac{\mathrm{1}}{{x}+\mathrm{2}}−\frac{\mathrm{1}}{{x}+\mathrm{3}}\leqslant\frac{\mathrm{3}}{\mathrm{4}}…

1-x-1-3-1-x-1-3-5-1-3-Find-x-

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Question Number 144760 by mathdanisur last updated on 28/Jun/21 $\sqrt[3]{1 + \sqrt{x}} + \sqrt[3]{1 - \sqrt{x}} = \sqrt[3]{5}$ $F i n d x = ?$ Answered by Olaf_Thorendsen last updated on 28/Jun/21 $Let α = \sqrt[3]{1 + \sqrt{x}} and β = \sqrt[3]{1 - \sqrt{x}}$ $$\alpha+\beta\:\:=\:\sqrt[{\mathrm{3}}]{\mathrm{5}} \…

Question-144767

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Question Number 144767 by mnjuly1970 last updated on 29/Jun/21 Answered by Rasheed.Sindhi last updated on 29/Jun/21 $$\left({x}^{\mathrm{3}} −\frac{\mathrm{2}}{{x}^{\mathrm{2}} }\right)^{{m}} ={a}_{\mathrm{0}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +…+{a}_{{n}} {x}^{{n}}…

Category: Algebra