Question

Real numbers a, b, c, and d satisfy property ab = 2cd. Which number can not be expressed as the product abcd?
a)50
b)100
c)200
d)450
e)800​

Answer 1

Answer:

b) 100 , because you 450=2*15^2 , its gives a real no solution

Answer 2

Given : ab = 2cd

To Find :  Which number can not be expressed as the product abcd?

a)50

b)100

c)200

d)450

e)800​

Solution:

abcd

ab =2cd

= 2cd  cd

= 2(cd)²

2(cd)² = 50

=> cd = ± 5

2(cd)² = 100

=> cd = ± 5√2

2(cd)² =200

=> cd = ± 10

2(cd)² =450

=> cd = ± 15

2(cd)² = 800

=> cd = ± 20

All can be expressed if a, b , c and d are real

But if a , b c  and d are rational numbers

Then  cd = ± 5√2   is not possible

Hence abcd can not be 100

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