Question

A number is divided strictly into two unequal parts such that the difference of the squares of the two parts equals 50 times the difference between the two parts. What is the number?​

Answer 1

A number is divided strictly into two unequal parts such that the difference of the squares of the two parts equals 50 times the difference between the two parts. What is the number?

answer : 50

solution : Let x and y are two parts of an unknown number. where x > y.

a/c to question,

the difference of the squares of the two parts equals 50 times the difference between the two parts.

i.e., (x² - y²) = 50(x - y)

or, (x - y)(x + y) - 50(x - y) = 0

or, (x - y) [(x + y) - 50] = 0

or, (x - y) ≠ 0 so, x + y - 50 = 0

⇒x + y = 50

hence, unknown number is (x + y) = 50.