Question

The difference of square of two natural numbers 88 if the larger number is 5 less than twice the smaller number then find the numbers

Answer 1

Let the numbers be x (smaller) and y (larger).

According to the problem,

y² - x² = 88 ... (i)
y = 2x - 5 ... (ii)

Substituting the value of y from the equation (ii) in equation (i), we get,

(2x - 5)² - x² = 88
⇒ 4x² - 20x + 25 - x² - 88 = 0
⇒ 3x² - 20x - 63 = 0
⇒ 3x² - 27x + 7x - 63 = 0
⇒ 3x (x - 9) + 7 (x - 9) = 0
⇒ (3x + 7) (x - 9) = 0

∴ Either x = 9 or x = - 7/3
But x cannot be negative.
So, x = 9
And, y = 2x - 5 = 2 × 9 - 5 = 18 - 5 = 13

Answer 2

łєт тнє sмαłłєя ησ: вє x
тнєη тнє łαяgєя ησ: ıs 2x - 5

gıѵєη ,

(2x - 5)² - x² = 88

4x² -20x + 25 - x² = 88

3x² - 20x - 63 = 0

3x² - 27x + 7x - 63

3x(x - 9) + 7(x - 9)

(3x + 7) (x - 9)

x = -7/3 . x = 9

тнє ѵαłυє cαηησт вє ηєgαтıѵє , нєηcє , x = 9 ıs тнє cσяяєcт ѵαłυє.

===========================

2x - 5 = 18 - 5 = 13
----------------------------------

тнє ησ:s αяє 9 αη∂ 13