Question

Compliting square rroot method by coefficient formula x2+2x-5 is equal to 0

Answer 1

The value of x =√6 - 1 is solved by Completing The Square

Step-by-step explanation:

To complete it with a square root method we will form a perfect square trinomial on the left side of the equation and then find the value of x.

Perfect Square trinomial is

(a+b)²= a²+2 ab+b²

Given : x²+2 x-5= 0

x²+ 2 x = 5..... (1)

By dividing the co-efficient of x (i.e) 2 by 2 and then squaring the result we get,

$\frac{2}{2} = 1 \\1^{2} = 1$

Adding the result (i.e) 1 on both the sides of the equation (1)

x² + 2 x +1 = 5 + 1

x² + 2 x + 1 = 6

The left side of the equation is a perfect  square trinomial

(x + 1)² = x² + 2x +1

∴ (x+1)² = 6

Taking square root on both the sides we get,

$\sqrt{ (\text{x}+1)^2} = \sqrt{6}$

x+1 = √6

∴ x = √6 -1

Hence the value of x =√6 - 1 is solved by Completing The Square.

To Learn More....

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