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If α and β are the roots of the ax^2 + 2bx + c = 0 and α + δ and β + δ are the roots of Ax^2 + 2Bx + C = 0 for some constant δ then prove that ((b^2 − ac)/a^2 ) = ((B^2 − AC)/A^2 ) .

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\: \\ $$$${ax}^{\mathrm{2}} \:+\:\mathrm{2}{bx}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{and}\:\alpha\:+\:\delta\:\mathrm{and}\:\beta\:+\:\delta\:\mathrm{are} \\ $$$$\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{Ax}^{\mathrm{2}} \:+\:\mathrm{2}{Bx}\:+\:{C}\:=\:\mathrm{0}\:\mathrm{for}\:\mathrm{some}\: \\ $$$$\mathrm{constant}\:\delta\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{{b}^{\mathrm{2}} \:−\:{ac}}{{a}^{\mathrm{2}} }\:=\:\frac{{B}^{\mathrm{2}} \:−\:{AC}}{{A}^{\mathrm{2}} }\:. \\ $$

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what is meant by ξ

$${what}\:{is}\:{meant}\:{by}\:\xi \\ $$

Question Number 202001 Answers: 1 Comments: 0

If a circle of radius r is inscribed in a triangl ABC. Express r in terms of a,b and c only

$${If}\:{a}\:{circle}\:{of}\:{radius}\:{r}\:{is}\:{inscribed}\:{in} \\ $$$${a}\:{triangl}\:{ABC}.\:{Express}\:{r}\:{in}\:{terms}\:{of} \\ $$$${a},{b}\:{and}\:{c}\:{only} \\ $$

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Solve ((1/x) − (1/x^3 ))^(1/2) + ((1/x^2 ) − (1/x^3 ))^(1/2) = 1

$$\boldsymbol{\mathrm{Solve}} \\ $$$$\left(\frac{\mathrm{1}}{{x}}\:−\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:+\:\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \:=\:\mathrm{1} \\ $$

Question Number 201989 Answers: 1 Comments: 0

Question Number 201952 Answers: 1 Comments: 0

(gof)_x =2x−1 (fog)_x ^(−1) =3x+2 (fof)_3 =?

$$\left({gof}\right)_{{x}} =\mathrm{2}{x}−\mathrm{1}\:\: \\ $$$$\left({fog}\right)_{{x}} ^{−\mathrm{1}} =\mathrm{3}{x}+\mathrm{2} \\ $$$$\left({fof}\right)_{\mathrm{3}} =? \\ $$

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Question Number 201941 Answers: 2 Comments: 1

x^4 −((17)/(18))x^2 +((40)/3)x+((1625)/(144))=0 Find roots. (Two are real and two are complex)★

$${x}^{\mathrm{4}} −\frac{\mathrm{17}}{\mathrm{18}}{x}^{\mathrm{2}} +\frac{\mathrm{40}}{\mathrm{3}}{x}+\frac{\mathrm{1625}}{\mathrm{144}}=\mathrm{0} \\ $$$${Find}\:{roots}.\:\left({Two}\:{are}\:{real}\:{and}\:{two}\:\right. \\ $$$$\left.{are}\:{complex}\right)\bigstar \\ $$

Question Number 201940 Answers: 1 Comments: 0

tan^3 (xy^2 +y)=x find (dy/dx)

$$\boldsymbol{{tan}}^{\mathrm{3}} \left(\boldsymbol{{xy}}^{\mathrm{2}} +\boldsymbol{{y}}\right)=\boldsymbol{{x}}\:\:\boldsymbol{{find}}\:\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}} \\ $$

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if (a−2)^2 = 4a find: 5a + 4 + ((16)/(5a + 4)) = ?

$$\mathrm{if}\:\:\:\left(\mathrm{a}−\mathrm{2}\right)^{\mathrm{2}} \:=\:\mathrm{4a} \\ $$$$\mathrm{find}:\:\:\:\mathrm{5a}\:+\:\mathrm{4}\:+\:\frac{\mathrm{16}}{\mathrm{5a}\:+\:\mathrm{4}}\:=\:? \\ $$

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$$ \\ $$

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