Question

x^2y,y^2z,z^2x find the fourth proportional​

Answer 1

Solution :

Let the fourth proportional be k .

Given :

Proportional 1 => x^2y

Proportional 2 => y^2z

Proportional 3 => z^2x

Proportional 4 => k .

Product of Antecedents = Product of Consequents .

=> [ x^2y ] × k = [ y^2z × z^2x ]

=> k = [ y^2z ] • [ z ^ 2x ] / [ x^ 2y ]

$\sf{ \bold { Hence \: , \: k = x^{ -2y } \times y ^ { 2z } \times z^{ 2x } }}$ .

This is the required value of the fourth proportional .

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