Question

( 2x + 1 )² + ( x + 1)² = 6x + 47​

Answer 1

Solution :

The given expression is :

> (2x + 1)² + (x + 1)² = 6x + 47

> [ 4x² + 4x + 1 ] + [ x² + 2x + 1 ] = 6x + 47

> 5x² + 6x + 2 = 6x + 47

> 5x² + 2 = 47

> 5x² = 45

> x² = 9

> x = ± 3.

This is the required answer.

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Additional Information :

(a + b)² = a² + 2ab + b²  

(a + b)² = (a - b)² + 4ab  

(a - b)² = a² - 2ab + b²  

(a - b)² = (a + b)² - 4ab  

a² + b² = (a + b)² - 2ab  

a² + b² = (a - b)² + 2ab  

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²  

ab = {(a + b)/2}² - {(a-b)/2}²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)  

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)  

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

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Answer 2

Answer:

➠ ( 2x + 1 )² + ( x + 1 )² = 6x + 47

➻ ( 2x)² + 2.2x.1 + ( 1 )² + ( x )² +2.x.1 + ( 1 )² = 6x + 47

➻ 4x² + 4x + 1 + x² + 2x + 1 = 6x + 47

➻ 5x² + 6x - 6x + 2 = 47

➻ 5x² + 2 = 47

➻ 5x² = 47 - 2

➻ 5x² = 45

➻ x² = 45/5

➻ x² = 9

➻ x = √3

➻ x = ±3

∴ The solution is x = 3 or x = - 3.