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Question Number 191451 Answers: 1 Comments: 0

x+(1/x)=5 and x∙y=4 find x^2 +((1/y))^2 =?

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{5}\:\:{and}\:{x}\centerdot{y}=\mathrm{4}\:{find} \\ $$$${x}^{\mathrm{2}} +\left(\frac{\mathrm{1}}{{y}}\right)^{\mathrm{2}} =? \\ $$

Question Number 191450 Answers: 0 Comments: 0

x+(1/x)=5 and x∙y=4 faind x^4 +((1/y))^3 =?

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{5}\:\:{and}\:\:{x}\centerdot{y}=\mathrm{4} \\ $$$${faind}\:\:\:\:{x}^{\mathrm{4}} +\left(\frac{\mathrm{1}}{{y}}\right)^{\mathrm{3}} =? \\ $$

Question Number 191445 Answers: 0 Comments: 0

Factorize (x − 998)(x − 999)−(((1000)/(999^2 )))

$$\mathrm{Factorize} \\ $$$$\left({x}\:−\:\mathrm{998}\right)\left({x}\:−\:\mathrm{999}\right)−\left(\frac{\mathrm{1000}}{\mathrm{999}^{\mathrm{2}} }\right) \\ $$

Question Number 191443 Answers: 2 Comments: 0

(3^(100) + 2^(100) ), 4^(100) which is greater? Give proof.

$$\left(\mathrm{3}^{\mathrm{100}} \:+\:\mathrm{2}^{\mathrm{100}} \right),\:\mathrm{4}^{\mathrm{100}} \:\mathrm{which}\:\mathrm{is}\:\mathrm{greater}? \\ $$$$\mathrm{Give}\:\mathrm{proof}. \\ $$

Question Number 191442 Answers: 0 Comments: 0

Question Number 191440 Answers: 0 Comments: 0

Question Number 191439 Answers: 0 Comments: 0

Question Number 191436 Answers: 1 Comments: 0

Factorize x^2 + (1/a) (bx + c)

$$\mathrm{Factorize} \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\boldsymbol{{a}}}\:\left(\boldsymbol{{bx}}\:+\:\boldsymbol{{c}}\right) \\ $$

Question Number 191435 Answers: 0 Comments: 0

It is given that I_1 =∫xg[x(1−x)]dx , I_2 = ∫g[x(1−x)]dx. Find (I_2 /I_1 ). Thanks.

$$\:{It}\:{is}\:{given}\:{that}\:{I}_{\mathrm{1}} =\int{xg}\left[{x}\left(\mathrm{1}−{x}\right)\right]{dx}\:,\: \\ $$$${I}_{\mathrm{2}} =\:\int{g}\left[{x}\left(\mathrm{1}−{x}\right)\right]{dx}.\:{Find}\:\frac{{I}_{\mathrm{2}} }{{I}_{\mathrm{1}} }.\:{Thanks}. \\ $$

Question Number 191410 Answers: 1 Comments: 0

Three villages A, B and C are on a straight road and B is the mid-way between A and C. A motor cyclist moving with a uniform acceleration passes A, B and C. The speeds with which the motorcyclist passes A and C are 20ms^(−1) and 40ms^− respectively. find the speed with which the motor cyclist passes B.

$$\:{Three}\:{villages}\:{A},\:{B}\:{and}\:{C}\:{are}\:{on}\:{a}\: \\ $$$$\:{straight}\:{road}\:{and}\:{B}\:{is}\:{the}\:{mid}-{way} \\ $$$${between}\:{A}\:{and}\:{C}.\:{A}\:{motor}\:{cyclist} \\ $$$${moving}\:{with}\:{a}\:{uniform}\:{acceleration} \\ $$$${passes}\:{A},\:{B}\:{and}\:{C}.\:{The}\:{speeds}\:{with}\: \\ $$$${which}\:{the}\:{motorcyclist}\:{passes}\:{A}\:{and}\: \\ $$$${C}\:{are}\:\mathrm{20}{ms}^{−\mathrm{1}} \:{and}\:\mathrm{40}{ms}^{−} \:{respectively}. \\ $$$${find}\:{the}\:{speed}\:{with}\:{which}\:{the}\:{motor} \\ $$$${cyclist}\:{passes}\:{B}. \\ $$

Question Number 191409 Answers: 1 Comments: 0