Question

sum of the square of a number and it's two third is 21 less than the square of its consecutive number.find the number​

Answer 1

Answer:

x = 15

Step-by-step explanation:

According to the given conditions,

Let's assume the number to be x, then we get,

x² + 2x/3 = (x+1)² - 21

x² + 2x/3 = x² + 2x + 1 - 21

=> 2x/3 = 2x - 20

=> 2x = (2x - 20)3

=> x = (6x - 60)/ 2

=> x = 3x - 30

Therefore 3x - x = 30

=> x = 30/2 = 15.

Verification

LHS

x² + 2x/3 = 15² + 2(15)/3 = 225 + 10 = 235.

RHS

(x + 1)² - 21 = (15 + 1)² - 21 = 16² - 21

= 256 - 21 = 235.

LHS = RHS

Hence proved