Question

Find two consecutive numbers whose squares, when subtracted, equals 43.

Answer 1

Answer:

21 and 22 are two consecutive numbers whose squares, when subtracted, equals 43.

Step-by-step explanation:

Let x, x+1 are two consecutive numbers

According to given Condition

$(x+1)^{2} - x^{2} = 43$

$-x^{2} +x^{2} +1 +2x = 43$

$2x = 43 - 1$

$x = \frac{42}{2}$

$x = 21$

$x + 1 =22$

21 and 22 are two consecutive numbers whose squares, when subtracted, equals 43.

Answer 2

Answer:

21 and 22

Step-by-step explanation:

let the 2 consecutive numbers be n and n + 1, then

(n + 1)² - n² = 43 ← expand (n + 1)² using FOIL

n² + 2n + 1 - n² = 43 ← collect like terms on left side

2n + 1 = 43 ( subtract 1 from both sides )

2n = 42 ( divide both sides by 2 )

n = 21

Thus the numbers are 21 and 22