if a and b be the roots of the equation x(2x + 1) = 1 then find the value of a^2 - b^2
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Answered by
2
x(2x+1)=1
2x^2+x=1
2x^2+x-1
2x^2+2x-x-1
2x(x+1) -1(x+1)
(2x-1) (x+1)
x=1/2. ,x=-1
(1/2)^2-(-1)^2
1/4-1
1-4/4
-3/4
2x^2+x=1
2x^2+x-1
2x^2+2x-x-1
2x(x+1) -1(x+1)
(2x-1) (x+1)
x=1/2. ,x=-1
(1/2)^2-(-1)^2
1/4-1
1-4/4
-3/4
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from this we can write the equation as 2x^2+x-1=0 we know that a^2-b^2 can be written as (a-b) (a+b)
we know that sum of the roots of the polynomial that is a+b = -b/a
from the polynomial a+b=-1/2 and a-b=√b^2-4ac/2a
substitute the values in the equation we get
a-b=3 then from the (a-b) (a+b) that is a^2-b^2
then that (3)(-1/4)equals to -3/4
Hence a^2-b^2=-3/4
we know that sum of the roots of the polynomial that is a+b = -b/a
from the polynomial a+b=-1/2 and a-b=√b^2-4ac/2a
substitute the values in the equation we get
a-b=3 then from the (a-b) (a+b) that is a^2-b^2
then that (3)(-1/4)equals to -3/4
Hence a^2-b^2=-3/4
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