Question

How to split x^2-4 by using middle term method

Answer 1

Question :

How to split x^2-4 by using middle term method

Solution :

Solve this question by using identity

a² - b² = (a+b)(a-b)

so,

= x² - 4

= (x)² - (2)²

= (x+2)(x-2)

Some important identities :

• (a+b)² = a² + b²+2ab
• (a-b)² = a²+b²-2ab
• a²-b² = (a+b)(a-b)
• a³-b³ =(a-b)(a²+ab+b²)
• (a+b)³ = a³+b³+3ab(a+b)
• (a-b)³ = a³-b³-3ab(a-b)

Answer 2

AnsWer :

x = 2 and -2.

Given :

• General equation ax²+bx+c =0.
• x²-4 = 0.
• The degree of given equation is 2, so we consider it have Quadratic equation.

Method Use,

• Quadratic Formula.
• Splitting the middle term.

Solution :

Let Try Alzebra,

we have Equation,

$\bullet \: \tt{x}^{2} - 4 = 0.$

$\implies \tt {x}^{2} = 4.$

$\implies \tt x = \sqrt{4} .$

$\implies \tt x = \pm2.$

Let try Quadratic formula,

$\bullet \tt x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Where as,

• a = 1.
• b = 0.
• c = -4.

Now, Putting all above value in Quadratic formula, We get.

$\tt \implies x = \frac{ - (0) \pm \sqrt{ {0}^{2} - 4 \times 1 \times - 4} }{2} .$

$\tt\implies x = \frac{ \pm \sqrt{16} }{2}$

$\tt \implies x = \frac{ \pm4}{2}$

$\tt \implies x = \frac{ \cancel4}{ \cancel2} \: \: \: \: \: \: \: \red{ or} \: \: \: \: \: \: \: x = \frac{ - \cancel 4}{ \cancel2}$

$\tt\implies \: x = 2 \: \: \: \: \: \: \red{or} \: \: \: \: \: \: x = - 2$

$\tt \implies x = \pm2.$

Therefore, the value of x²-4=0 is 2 and -2.