Question

The difference between the square of a natural number, x, and the square of its preceding number is
17. Find x.
​

Answer 1

Given:-

• Difference between the square of natural number "x" and the square of its preceding number is 17.

To find:-

• The value of "x"

Answer:-

▪ Square of x = x²

▪ Preceding number of x = (x - 1)

▪ Square of preceding number of x = (x - 1)²

Accroding to the question,

Difference between the square of natural number "x" and the square of its preceding number is 17.

So,

$\sf {x}^{2} - {(x - 1)}^{2} = 17$

• Using (a - b)² = a² + b² - 2ab with a = x and b = 1,

$\sf \longrightarrow {x}^{2} - \{ {x}^{2} + {1}^{2} - (2 \times x \times 1) \} = 17$

$\sf \longrightarrow {x}^{2} - \{ {x}^{2} + {1}^{2} - 2x \} = 17$

$\sf \longrightarrow {x}^{2} - {x}^{2} - 1 + 2x = 17$

$\sf \longrightarrow \cancel{{x}^{2}} \: \: \cancel{ - {x}^{2}} - 1 + 2x = 17$

$\sf \longrightarrow - 1 + 2x = 17$

$\sf \longrightarrow 2x = 18$

$\sf \longrightarrow x = \dfrac{18}{2}$

$\longrightarrow \underline{ \underline{ \sf{ \green{ x = 9}}}}$