Q. 255.0( 1 Vote )

Does the followin

Answer :

We know,



Now,




[ tan-1(-x) = -tan-1x]



-7 + 7x = 2x2 – 2x + 2


2x2 – 9x + 9 = 0


2x2 – 6x – 3x + 9 = 0


2x(x – 3) – 3(x – 3) = 0


(2x – 3)(x – 3) = 0



OR


a*b = ab + 1,


Let p, q Q,


p*q = pq + 1 Q


As, P*Q also belong to Q, * defined on Q is binary operation.


Commutative:


Let p, q Q,


p*q = pq + 1


q*p = qp + 1


As,


pq = qp


pq + 1 = qp + 1


p*q = q*p


* satisfies commutative property!


Associativity:


Let p, q, r Q,


Here,


(p*q)*r = (pq + 1)*r


= (pq + 1)r + 1


= pqr + r + 1


and


p*(q*r) = p*(qr + 1)


= p(qr + 1) + 1


= pqr + p + 1


(p*q)*r = p*(q*r)


(*) doesn’t satisfy associative property!


Identity:


Let identity be e, then p*e = p


pe + 1 = p


pe = p – 1



As, identity is not unique, the binary operation don’t have a identity and as identity is not there, inverse is absurd!


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