Q. 255.0( 1 Vote )

# Does the followin

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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