Question

x '2 – 2ax – (4b'2 – a'2) = 0 solve for x

Answer 1

equation is x² - 2ax -(4b² -a²) =0
rearrange the terms,
(x² -2ax +a²) = 4b²
⇒(x -a)² = (2b)²
⇒(x -a) =2b or, (x -a) = -2b
⇒x = (a +2b) or x= (a -2b)

Answer 2

The required solution is x = a - 2b , a + 2b

Correct question : x² - 2ax - (4b² - a²) = 0 solve for x

Given :

x² - 2ax - (4b² - a²) = 0

To find :

To solve for x

Formula Used :

• (a - b)² = a ² - 2ab + b²

• a² - b² = (a + b) (a - b)

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

x² - 2ax - (4b² - a²) = 0

Step 2 of 2 :

Find the value of x

x² - 2ax - (4b² - a²) = 0

⇒ x² - 2ax - 4b² + a² = 0

⇒ x² - 2ax + a² - 4b² = 0

⇒ (x - a)² - 4b² = 0 [ ∵ (a - b)² = a ² - 2ab + b² ]

⇒ (x - a)² - (2b)² = 0

⇒ (x - a + 2b)(x - a - 2b) = 0 [ ∵ a² - b² = (a + b) (a - b) ]

Now ,

(x - a + 2b) = 0 gives x = a - 2b

(x - a - 2b) = 0 gives x = a + 2b

Hence the required solution is x = a - 2b , a + 2b

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