The…...…of all the cube roots of unity is zero,i.e.,1+w+w2=0
a)product
b)sum
c)division
d) all of these
The ……of all the cube roots of unity is one, i.e. 1.w.w2=1
a)product
b)sum
c)division
d) all of these
If α=1 , β=2 then the value of α3+β3+3αβ is
a) 14
b)15
c) 16
d)17
Solution:α3+β3+3αβ
α=1 , β=2 = (1)3+(2)3+3(1)(2)
1+8+6 =15
The product of two consecutive natural numbers is 72. Find the numbers.
a) 4, 5
b) 7, 11
c) 8, 9
The sum of the
squares of two consecutive natural numbers is 313. Find the numbers.
a) 12, 13
b) 21, 29
d) 23, 31
The sum of two numbers is 11 and sum of their square is 65. Find
the numbers?
a) 4, 7
b) 7, 9
c) 11, 3
d) 2, 7
Solution:let the first no is x
So the second no is (11-x)
According to question
x2+(11-x)2=65 x2+121+x2-22x=65
2x2-22x+56=0divide the equation by 2
x2-11x+28=0 x2-7x-4x+28=0
x(x-7)-4(x-7)=0 (x-7)(x-4)=0
(x-7)=0 x=7
(x-4)=0 x=4
So the No are 4 and 7
