Question

the difference of squares of two numbers is 204 .the square of the smaller number is 4 less than 10 times the larger number. find the two numbers.​

Answer 1

Step-by-step explanation:

this is the required answer you want

X=20 and y=14

Answer 2

Answer:

The numbers are 14 and 20

Step-by-step explanation:

Given:

Difference of squares of two numbers = 204

Square of the smaller number is 4 less than 10 times the larger number

Let the smaller number be 'x' and the larger number be 'y'

Therefore, according to the conditions given in the question,

y² - x² = 204 => y² - 204 =  x²  

x² = 10y - 4

Solving the above equations by equating,

y² - 204 = 10y - 4

=> y²- 10y = 204 - 4

=> y²- 10y = 200

=> y²- 10y - 200 = 0

=> y²- 20y + 10y - 200 = 0

=> y(y - 20) + 10(y - 20) = 0

=> (y - 20) (y + 10) = 0

=> y - 20 = 0 or y + 10 = 0

=> y = 20 or y = -10

As x² = 10y - 4

=> x² = 10*20 - 4  or x² = 10*(-10) - 4

=> x² = 200 - 4  or x² = -100 - 4

=> x² = 196  or x² = -104

Since the square of a number cannot be negative, therefore, x² = 196

=> x = 14

and 20 > 14

Therefore, the smaller number = x  = 14

and the larger number = y  = 20

Therefore, the numbers are 14 and 20