Question

find two consecutive numbers whose square have sum 85​

Answer 1

Step-by-step explanation:

Given:

• Sum of square of two consecutive numbers is 85.

To Find:

• What are the two numbers?

Solution: Let the two consecutive even natural numbers be x and x + 1

• Square of these numbers = (x)² and (x + 1)² •

A/q

$\small\implies{\sf }$ (x)² + (x + 1)² = 85

$\small\implies{\sf }$ x² + x² + 1 + 2x = 85 [ (a + b)² = a² + b² + 2ab ]

$\small\implies{\sf }$ 2x² + 2x + 1 – 85 = 0

$\small\implies{\sf }$ 2x² + 2x – 84 = 0

$\small\implies{\sf }$ 2 (x² + x – 42) = 0

$\small\implies{\sf }$ x² + 7x – 6x – 42 = 0

$\small\implies{\sf }$ x (x + 7) – 6 (x + 7) = 0

$\small\implies{\sf }$ (x – 6) (x + 7)

Hence, x = 6 or x = 7

★ Case I = If 6x + 1 = 6 + 1 = 7

★ Case II = If 7x + 1 = –7 + 1 = –6

So, The consecutive numbers whose square have a sum of 85 can be 6 and 7 or –6 and –7

Answer 2

A N S W E R :

• The two consecutive numbers -7, -6

Given :

• Sum of square of two consecutive numbers is 85

To find :

• Find the two numbers ?

Solution :

• Let one number be x

According to the question,

=> x² + (x + 1)² = 85

=> x² + x² + 1 + 2x = 85

=> 2x² + 2x + 1 = 85

=> 2x² + 2x - 84 = 0

=> x² + x - 42 = 0

=> x² + 7x - 6x - 42 = 0

=> x(x + 7) - 6(x + 7) = 0

=> (x - 7)(x + 7) = 0

Therefore,

• x = 6, -7

• x = 6

Then,

• The numbers are 6 and 7

=> x = -7

Hence,

• The two consecutive numbers -7, -6