Question

given that a=3,b= -2, and c= -4, evaluate (a + 2b)2square - 4c

Answer 1

Answer:

We have, ab

2

c

3

,a

2

b

3

c

4

,a

3

b

4

c

5

are in A.P

Now, A.M≥G.M

⇒

3

a+b+c

≥(abc)

1/3

⇒a+b+c≥3

1/3

(abc)

1/3

but given ab

2

c

3

,a

2

b

3

c

4

,a

3

b

4

c

5

are in A.P (∵abc



=0).

Hence,

2a

2

b

3

c

4

=ab

2

c

3

+a

3

b

4

c

5

2abc=1+a

2

b

2

c

2

⇒(abc−1)

2

=0

Now eq(1) we get

a+b+c≥3(1)

1/3

⇒(a+b+c)≥3

Hence, minimum value of a+b+c is 3