Question

The product of three consecutive positive numbers (x - 1), x and (x + 1) is 96 times their sum.

(i) Use this information to form an equation in x and show that it simplifies to x² - 289x = 0,

(ii) Solve the equation x - 289x = 0 to find the three numbers.

please I need it under 20min ​
don't answer it if you don't know thanks

Answer 1

Explanation:

their sum is

x - 1 + x + x + 1 = 3x

their product is

(x - 1)x(x + 1) = x(x² - 1)

96 × 3x = x(x² - 1)

96 × 3 = x² - 1

288 = x² - 1

x² = 289

x = 17

so, the solution is 16, 17, 18