Question

The deffrence between square of two consecutive natural number is 37 then find the smaller number

Answer 1

AnswEr :

Let the First No. be x then Second No. will be (x + 1) as both are consecutive natural no.

• According to the Question Now :

⇒ (Second No.)² - (First No.)² = 37

⇒ ( x + 1 )² - ( x )² = 37

• (a + b)² = a² + b² + 2ab

⇒ ( x² + 1 + 2x ) - x² = 37

⇒ x² + 1 + 2x - x² = 37

• Both x² will be cancelled

⇒ 1 + 2x = 37

⇒ 2x = 37 - 1

⇒ 2x = 36

• Dividing Both term by 2

⇒ x = 18

◗ First No. = x = 18

◗ Second No. = (x + 1) = (18 + 1) = 19

∴ Natural Numbers will be 18 and 19.

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• Verification :

⇝ (Second No.)² - (First No.)² = 37

⇝ ( x + 1 )² - ( x )² = 37

⇝ (18 + 1)² - (18)² = 37

⇝ (19)² - (18)² = 37

• (a² - b²) = (a + b)(a - b)

⇝ (19 + 18)(19 - 18) = 37

⇝ 37 × 1 = 37

⇝ 37 = 37 Hence, Verified!

Answer 2

Given :----

• Difference b/w square of two consecutive natural numbers is 37.

To Find :---

• Smaller number ?

Formula used :---

• (a+b)² = a² + 2ab + b²

solution :-----

Let the smaller number be x ,

than next natural number be (x+1).

A/q,

(x+1)² - (x²) = 37

→ (x²+1 + 2x) - x² = 37

→ x² - x² + 2x + 1 = 37

→ 2x + 1 = 37

→ 2x = 37 - 1

→ 2x = 36

→ x = 36/2 = 18 (Ans)

so, our smaller natural number will be 18 ..

(Hope it helps you)