Question

Equation (x+1)2 – x2 = 0 has _____ real root(s).

Answer 1

Answer:

1 root

Step-by-step explanation:

(x+1)^2 – x^2 = 0 =>

x^2+2x+1-x^2=0

2x+1=0

x=0.5

Answer 2

(x + 1)² - x² = 0 has one real root

Given :

The equation (x + 1)² - x² = 0 has _____ real root(s)

To find :

Fill in the blank

Solution :

Step 1 of 3 :

Write down the given equation

The given equation is

(x + 1)² - x² = 0

Step 2 of 3 :

Simplify the given equation

$\displaystyle \sf{ {(x + 1)}^{2} - {x}^{2} = 0 }$

$\displaystyle \sf{ \implies {x}^{2} + 2x + 1 - {x}^{2} = 0 }$

$\displaystyle \sf{ \implies 2x + 1 = 0 }$

Step 3 of 3 :

Find number of real roots

$\displaystyle \sf{ {(x + 1)}^{2} - {x}^{2} = 0 }$

$\displaystyle \sf{ \implies 2x + 1 = 0 }$

$\displaystyle \sf{ \implies 2x = - 1 }$

$\displaystyle \sf{ \implies x = - \frac{1}{2} }$

Hence (x + 1)² - x² = 0 has one real root

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