Question

here are (4x^4-20x^2y^2+25y^4)students to be arranged in a field during assembly of a school. Find the number of rows and columns in which these students can be arranged such that no student is left out.

Answer 1

Answer:

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Let the number of rows be x rows and the number of students in each row be y students .

Then the total number of students in a class =xy students.

∴ According to the question ,

(x−2)(y+1)=xy

⇒xy+x−2y−2=xy

x−2y=2 .....(i)

And

(x+3)(y−1)=xy

⇒xy−x+3y−3=xy

−x+3y=3 .....(ii)

x−2y=2

−x+3y=3

On adding , y=5 students.

putting the value of y in equation .......(i)

x−2(5)=2

x=12 rows.

∴ Total number of students in a classroom =(12×5)students =60 students.