Question and Answers Forum

AlgebraQuestion and Answers: Page 320

Question Number 42030 Answers: 4 Comments: 1

x+(1/x)=5 x^5 +(1/x^5 )=?

$x + \frac{1}{x} = 5 x^{5} + \frac{1}{x^{5}} = ?$

Question Number 42009 Answers: 1 Comments: 0

if (a+bω+cω^2 )+(aω+bω^2 +c)^2 +(aω^2 +b+cω)^2 =0 then prove that a=c or a+c=2b

$if (a + b ω + c ω^{2}) + {(a ω + b ω^{2} + c)}^{2} + {(a ω^{2} + b + c ω)}^{2} = 0$ $then prove that a = c or a + c = 2 b$

Question Number 41985 Answers: 1 Comments: 1

Prove e^x ≥x+1 ∀x∈R in as many ways as you can show

$Prove e^{x} ⩾ x + 1 \forall x \in R in as many ways$ $as you can show$

Question Number 41984 Answers: 2 Comments: 7

solve simultaneously: 2(√k) + h = 9 ....... (i) k + 2(√h) = 3 ....... (ii)

$solve simultaneously : 2 \sqrt{k} + h = 9 . . . . . . . (i)$ $k + 2 \sqrt{h} = 3 . . . . . . . (ii)$

Question Number 41957 Answers: 1 Comments: 1

Question Number 41912 Answers: 2 Comments: 0

The estimated time for Abu and Ali to repair a faulty car is six hours. If Abu used 10 hours to repair the car, how many hours will Ali use to repair the car?

$The estimated time for Abu and Ali to repair a$ $faulty car is six hours . If Abu used 10 hours to$ $repair the car, how many hours will Ali use to repair$ $the car ?$

Question Number 41921 Answers: 2 Comments: 0

Find x : 625^(x − 5) = 200((√x))^3

$Find x : 625^{x - 5} = 200 {(\sqrt{x})}^{3}$

Question Number 41879 Answers: 1 Comments: 0

If a fraction is added to its denominator , it reduces to (1/2) and when the same fraction added to numerator, it also reduces to (2/3) (a) what is the fraction (b) find the square root such that the result of the fraction is less than 1

$If a fraction is added to its denominator, it reduces to \frac{1}{2} and$ $when the same fraction added to numerator, it also reduces to \frac{2}{3}$ $(a) what is the fraction$ $(b) find the square root such that the result of the fraction is less$ $than 1$

Question Number 41877 Answers: 1 Comments: 0

The tens digit of a two digit number is 3 greater than the units digit. When the digits are reversed, the number is reduced by 27. what is the number ?

$The tens digit of a two digit number is 3 greater than the units digit .$ $When the digits are reversed, the number is reduced by 27 .$ $what is the number ?$

Question Number 41866 Answers: 1 Comments: 0

Question Number 41860 Answers: 0 Comments: 2

(1,2,3,........100)are given number find the value of Σ(1×2)

$(1, 2, 3, . . . . . . . . 100) a r e g i v e n n u m b e r$ $f i n d t h e v a l u e o f Σ (1 \times 2)$

Question Number 41813 Answers: 1 Comments: 0

Any workings for this simultaneous equation ? x^x + y^y = 31 ........ equation (i) x + y = 5 ........ equation (ii)

$Any workings for this simultaneous equation ?$ $x^{x} + y^{y} = 31 . . . . . . . . equation (i)$ $x + y = 5 . . . . . . . . equation (ii)$

Question Number 41798 Answers: 0 Comments: 5

Solve: x^3 − 3x + 4 = 0 how can i know when to use: let x = y + (1/y)

$Solve : x^{3} - 3 x + 4 = 0$ $how can i know when to use : let x = y + \frac{1}{y}$

Question Number 41720 Answers: 0 Comments: 2

Difference of last two digits of 2019^(2019^(2019) ) is ?

$Difference of last two digits of 2019^{2019^{2019}} is ?$

Question Number 41710 Answers: 2 Comments: 0

Factorize: 60x^3 y + 115x^2 y^2 − 120xy^3

$Factorize : {60 x}^{3} y + {115 x}^{2} y^{2} - {120 xy}^{3}$

Question Number 41622 Answers: 4 Comments: 9

let z_1 and z_2 the roots of x^2 −2x+2=0 1) calculate z_1 ^3 +z_2 ^3 then (1/z_1 ^3 ) +(1/z_2 ^3 ) 2) calculate z_1 ^4 +z_2 ^4 then (1/z_1 ^4 ) +(1/z_2 ^4 ) 3) let n from N simplify A_n = z_1 ^n +z_2 ^n and B_n = z_1 ^n −z_2 ^n 4) simplify S_n =Σ_(k=0) ^(n−1) (z_1 ^k +z_2 ^k )

$l e t z_{1} a n d z_{2} t h e r o o t s o f x^{2} - 2 x + 2 = 0$ $1) c a l c u l a t e z_{1}^{3} + z_{2}^{3} t h e n \frac{1}{z_{1}^{3}} + \frac{1}{z_{2}^{3}}$ $2) c a l c u l a t e z_{1}^{4} + z_{2}^{4} t h e n \frac{1}{z_{1}^{4}} + \frac{1}{z_{2}^{4}}$ $3) l e t n f r o m N s i m p l i f y$ $A_{n} = z_{1}^{n} + z_{2}^{n} a n d B_{n} = z_{1}^{n} - z_{2}^{n}$ $4) s i m p l i f y S_{n} = \sum_{k = 0}^{n - 1} (z_{1}^{k} + z_{2}^{k})$