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1. If x = 2 + √3 and xy = 1, then the value of x2 + y2 is ?

2. If a – b, a and a + b are the zeroes of the polynomial x3 – 3x2 + x + 1, then the value of a + b can be :-
a) -1-√2
b) 1+ √2
c) -1+√2
d) 3

3. The Expression (x-y)3 - (X3-y3) is equal to :-
a) 2x2 – 3x2y + 3xy2 + 2y2
b) 3xy (y-x)
c) 3xy (x-y)
d) 2x2 – 3x2y + 3xy2

4. If α, β and γ are the zeroes of the polynomial x3 + px2 + qx + 2 , such that αβ + 1, then the value of 2p – q – 3 is ?

Profile image of Venkat Nihal
13 Years agoGrade Select Grade
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4 Answers

Profile image of Shaurya Gupta
13 Years ago

Q2: (a-b)+(a)+(a+b)=-b/a=3/1

      a=1

Now,

      (a+b)(a-b)(a) = -d/a=-1

      1-b2 = -1

       b= 21/2

    therefore a+b = 1+root2

Profile image of Shaurya Gupta
13 Years ago

3: (x-y)3= x3-3x2y+3xy2-y3                     -1

     x3-y3 = (x-y)(x2+xy+y2)                -2

therefore,

 1-2=  3xy(y-x)

Profile image of Shaurya Gupta
13 Years ago

1. Substitute x''s value in xy=1.

y will come 2-root3

there fore x2+y2 = 14

As for the 4rth question 

"such that  αβ + 1" what?..such that what?


Profile image of varun a
13 Years ago

1.7,;y=-2+/3