Question

4x²+4x+1=0 solve the equation

Answer 1

Given,

4x² + 4x + 1 =

4x² + 2x + 2x + 1 = 0

2x(2x+1) + 1(2x+1) = 0

(2x+1)(2x+1) = 0

(2x+1)² = 0

2x + 1 = 0

x = -1/2

Aliter;-

4x² + 4x + 1 =0

(2x)² + 1² + 2*(2x)*1 = 0

(2x+1)² = 0 ...........( (a+b)² = a² + b² + 2ab )

x = -1/2

Answer 2

Answer:

Solution of equation 4x²+4x+1=0 is x=$- \frac{1}{2}$

Step-by-step explanation:

Given,

$4{x}^{2} + 4x + 1 = 0$

By Middle term process we can solve this equation.

Now,

$4 {x}^{2} + 4x + 1 = 0 \\ 4 {x}^{2} + (2 + 2)x + 1 = 0 \\ 4 {x}^{2} + 2x + 2x + 1 = 0 \\ 2x(2x + 1) + (2x + 1) = 0 \\ (2x + 1)(2x + 1) = 0 \\ {(2x + 1)}^{2} = 0 \\ 2x + 1 = 0 \\ 2x = - 1 \\ x = - \frac{1}{2}$

Required Solution of the equation is $- \frac{1}{2}$

Some important formulas of Algebra,

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

${a}^{2} - {b}^{2} = (a + b)(a - b)\\{a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab\\{a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab\\{a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )\\{a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$