Capgemini Algebra Questions and Answers Quiz-1

1/2x +1/4x+1/8x=14.
Take x as common so you will get
(1/2 +1/4+1/8)x=14,
(7/8)x=14,
x=16.

Discriminant = b² - 4ac

Given that a = 2k, b = 5k, c = 2

b² - 4ac = 0

(5k)² - 4(2k)(2) = 0

25k² - 16k = 0

k(25k - 16) = 0

k = 0 or 25k - 16 = 0

k = 0 or k = 16/25

Answer: k = 0 or k = 16/25

given, (m⁶ + m⁴ + m² + 1)/m³

(m⁶/m³ + m⁴/m³ + m²/m³ + 1/m³)

(m³ + m + 1/m + 1/m³)

now,

m = (2 - √3)------------( 1 )

m³ = (8 - 3√3 - 6√3(2 - √3)

m³ = (8 - 3√3 - 12√3 + 18)

m³ = (26 - 15√3)-----------( 2 )

1/m = 1/(2 - √3) * (2 + √3)/(2 + √3)

1/m = (2 + √3)/(4 - 3)

1/m = (2 + √3)------------( 3 )

1/m³ = 1/(26 - 15√3) * (26 + 15√3)/(26 + 15√3)

1/m³ = (26 + 15√3)/(676 - 675)

1/m³ = (26 + 15√3)-------------( 4 )

adding------( 1 ) , --------( 2 ) , --------( 3 ) & --------( 4 )

(m + 1/m + m³ + 1/m³)

= (2 - √3 + 2 + √3 + 26 - 15√3 + 26 + 15√3)

= (4 + 52)

= 56

Hence, (m⁶ + m⁴ + m² + 1)/m³ = 56

 

(a-b)² = 4

(a-b) =  2

Here,12+4 is 16 and it is written as 2⁴, then 12/4 is 3,
so now it is 2¹² so answer is 4096.

As this equation should be divisible by a number for all Integral values, Assume n=1
(7^2)-(3^3) = 22
above equation is divisible by 22

s(s+s1+s2)=9
s= \frac{9}{s+s1+s2}
s1=\frac{16}{s+s1+s2}
s2=\frac{144}{s+s1+s2}
(s+s1+s2)^{2}=169
(s+s1+s2)=13

SO, S=9/14 ; S1=16/13 ; S2=144/13

3481

(x + 1/x) = 6

x^{2}+\frac{1}{x^{2}}=34 , x^{3}+\frac{1}{x^{3}}=198
(x^{2}+\frac{1}{x^{2}}) (x^{3}+\frac{1}{x^{3}})= 198*34
x^{5}+\frac{1}{x^{5}}=6726