Write the square of 25 as sum of two consecutive natural numbers?

1.	Write the square of 25 as sum of two consecutive natural numbers?
Answer» Answer: Equation : x² + (x + 1)² = 25 ✬ Given: SUM of squares of two consecutive natural NUMBERS is 25. To Show: In form of quadratic equation. Solution: Let first consecutive natural number be x. Therefore, ➟ Second consecutive number = (x + 1) Now, Square of first number = (x)² Square of 2ND number = (x + 1)² A/q Sum is 25. ➯ Equation = (x)² + (x + 1)² = 25 Hence option A is CORRECT. _______________________ x² + (x + 1)² = 25 x² + (x² + 1² + 2•x•1) = 25 x² + x² + 1 + 2x = 25 2x² + 2x = 25 – 1 2x² + 2x = 24 2x² + 2x – 24 = 0 2(x² + x – 12) x² + x – 12 Now, break this by Middle TERM splitting ➙ x² + x – 12 ➙ x² + 4x – 3x – 12 ➙ x(x + 4) – 3 (x + 4) ➙ (x – 3) (x + 4) ➙ x – 3 = 0 or, x + 4 = 0 ➙ x = 3 or x = –4 We will take positive value of x. { Negative ignored } So, The two consecutive natural numbers are ➮ First number = x = 3 ➮ Second number = x + 1 = 3 + 1 = 4 Step-by-step explanation:

Answer»

Answer:

Equation : x² + (x + 1)² = 25 ✬

Given:

SUM of squares of two consecutive natural NUMBERS is 25.

To Show:

In form of quadratic equation.

Solution: Let first consecutive natural number be x. Therefore,

➟ Second consecutive number = (x + 1)

Now,

Square of first number = (x)²

Square of 2ND number = (x + 1)²

A/q

Sum is 25.

➯ Equation = (x)² + (x + 1)² = 25

Hence option A is CORRECT.

_______________________

x² + (x + 1)² = 25

x² + (x² + 1² + 2•x•1) = 25

x² + x² + 1 + 2x = 25

2x² + 2x = 25 – 1

2x² + 2x = 24

2x² + 2x – 24 = 0

2(x² + x – 12)

x² + x – 12

Now, break this by Middle TERM splitting

➙ x² + x – 12

➙ x² + 4x – 3x – 12

➙ x(x + 4) – 3 (x + 4)

➙ (x – 3) (x + 4)

➙ x – 3 = 0 or, x + 4 = 0

➙ x = 3 or x = –4

We will take positive value of x. { Negative ignored }

So, The two consecutive natural numbers are

➮ First number = x = 3

➮ Second number = x + 1 = 3 + 1 = 4

Step-by-step explanation:

Discussion