Question

Please solve, don't spam please help PRMO is approaching​

Answer 1

Answer:

Hello My Friend!

Maximum Value is ¼ (1/4)

Step-by-step explanation:

ab+bc+cd

= ab+c(b+d)

= ab+ad+c(b+d)-ad

=a(b+d) + c(b+d) -ad

=(a+c)(b+d)-ad ----------[1]

Then, to maximize eq-1, we try maximize (a+c)(b+d) and maximize ad with contradiction to each other.

for ad , min. value is 0 (since negetive is not possible) , So either a or d must be zero.

for (a+c)(b+d),

let, X= a+c , Y= b+d

then we have to find maximum value of xy when X+Y=1, which we can prove that xy will be maximum when X=Y , so we conclude

X=Y=½

=>a+c=b+d=½

To maximize eq.1 , we have

ad=0

and

a+c=b+d=½

By trial and error method,, we can let a=d=0 (by ad=0),

so, b=c=½

now, by given equation,

ab+bc+cd

=0.½+½.½+½.0

=0+¼+0

=¼

That's all!!!

Hope it helps :-)