Question

if a1 a2 a3 a4 are positive real numbers such that a1 + a2 + a3 + a4 = 16 then find maximum value of (a1 + a2)(a3 + a4)

Answer 1

Maximum value can be obtained when a1=a2=a3=a4 =k (assume)

Now, 4k=16

This implies k=4

Now max value= (4+4)*(4+4) =64

Answer 2

Answer:

64

Step-by-step explanation:

Given that ,

If   a1 a2 a3 a4 are positive real numbers such that a1 + a2 + a3 + a4 = 16 than find maximum value of ( a1 + a2 ) ( a3 + a4 ).

So,

as per given condition.

a1 + a2 + a3 + a4 = 16

And

( a1 + a2 ) ( a3 + a4 )

Now,

we have to focus only on the terms

( a1 + a2 ) and  ( a3 + a4 ).

here are two condition that ,

multiply of ( a1 + a2 ) and ( a3 + a4 ) is maximum

and sum of a1, a2, a3, and a4 = 16.

Here take a example ,

a) 1 × 7 = 7 ,     1 + 7 = 8

b) 2 × 6 = 12 ,  2 + 6 = 8

c) 3 × 5 = 15  ,  3 + 5 = 8

d) 4 × 4 = 16  ,  4 + 4 = 8

From the above example we can conclude that ,

the multiply of number which is equal in their number have heigher multiple value.

So,

taking a1 = a2 = a3 = a4.

a1 + a2 + a3 + a4 = 16

a1 + a1 + a1 + a1 = 16

4a1 = 16

a1 = 4.

Now every value is 4.

Then the maximum value of the expression

( a1 + a2 ) ( a3 + a4 ).

= ( 4 + 4 ) ( 4 + 4 )

= 8 × 8

= 64.

Therefore, the heighest value of  ( a1 + a2 ) ( a3 + a4 ) is 64.

THANKS.

#SPJ2.

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