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Category: Algebra

Question-12257

Question Number 12257 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 Answered by sma3l2996 last updated on 17/Apr/17 $$\left({a}+{b}−\mathrm{2}{ab}\right)^{\mathrm{2}} +\left({a}+{b}−\mathrm{1}\right)^{\mathrm{2}} =\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\mathrm{4}{a}^{\mathrm{2}} {b}^{\mathrm{2}} −\mathrm{4}{ab}^{\mathrm{2}} +\mathrm{2}{a}\left({b}−\mathrm{2}{ab}\right)\right)+\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}}…

Question-12255

Question Number 12255 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 16/Apr/17 Answered by mrW1 last updated on 16/Apr/17 (x+1)(x+2)(x+3)(x+4)+1=(x+5232)(x+5212)(x+52+12)(x+52+32)+1$$=\left[\left({x}+\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} \right]\left[\left({x}+\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} \right]+\mathrm{1}…