Algebra Quiz-1

Investment in share bazar = 30%

Investment in Bitcoin = 70%

70% of x = 34000 + 30% of x
70x/100 = 34000 + 30x/100
70x100 -30x/100 = 34000
40x/100 = 34000
so, x = 85000 Rs

x-y=8-------(1)

(x-y)(x+y)=160------(2)

(8)(x+y)=160

x+y=\frac{160}{2}

x+y=20-->2

Add equation 1 and 2 we get

2x=28 then x=14

Sub x value in equation 1 we get 14-y=8, then y = 6

Two numbers are 14 and 6

f(X=0) = 0

f(X=1) = 2 \times 1 - 1 + f(1-1) = 2 - 1 + 0 = 1<br /> <br /> f(X=2) = 2 \times 2 - 1 + f(2-1) = 4 - 1 + 1 = 4<br /> <br /> f(X=3) = 2 \times 3 - 1 + f(3-1) = 6 - 1 + 4 = 9<br /> <br /> => f(X=n) = n^{2}

f(f(X)) = 81

X = \sqrt{\sqrt{81}} = 3

The required equation is:
=> x² - (sum of roots)x + product of roots = 0
=> x² - (4+5)x+4 × 5 = 0
=> x² - 9x + 20 = 0

By trail and error method, substitute the value of n from the options given below

Putting n=3

xⁿ - 27 = (x-3)(x²+3x+9)

\frac{x^{n}-27}{x-3} = \frac{x^{n}-3^3}{x-3}

Putting n=3,

= \frac{x^{3} - 3^{3}}{x-3} = \frac{(x-3)(x^{2} - 3x + 9)}{x-3}

x³+y³ = (x + y) × (x² − xy + y²)

Putting given values of x³+y³ and (x + y)

9 = 3 × ((x+y)² − 3xy)

= 3 × (9 − 3xy)

= 27 − 9xy

9xy = 18

xy = 2

x⁴ + y⁴ = (x² + y²)² - 2x²y²

= (x² + y²)² - 2 \times 4

[Putting value of xy] = ((x + y)² - 2xy)² - 2 \times 4

[Putting values of (x+y) and xy] = (9 - 4)² - 2 \times 4 = 17

8^{-1} \times X = 4^{-1}
\frac{1}{8} \times X = \frac{1}{4}
X = \frac{8}{4}
X = 2

(x-a)×(x-b)×(x-c)×...........×(x-z) = (x-a)×(x-b)×(x-c)×...........(x-x)×(x-y)×(x-z)

Since (x-x)=0 so, whole product is zero

(x-a)×(x-b)×(x-c)×...........×(x-z)= 0

Xn = Y

3n = 40.5, n= 13.5

4n = 96, n = 24

5n = 187.5, n=37.5

6n=324, n=54

for first 2 value of n = 24 - 13.5 == 10.5

for next 2 difference = 37.5 - 24 == 13.5

for next 2 difference = 54 - 37.5 == 16.5

The value difference between each is 3.

so the value of n = 3