Question

if a+b=12, ab=4, find a-b​

Answer 1

Answer :-

The value of a - b is 8√2.

Solution :-

We know that

(a - b)² = (a + b)² - 4ab

Here

• a + b = 12

• ab = 4

By substituting the values

⇒ (a - b)² = 12² - 4(4)

⇒ (a - b)² = 144 - 16

⇒ (a - b)² = 128

⇒ a - b = √128

⇒ a - b = √64 * √2

⇒ a - b = 8 * √2

⇒ a - b = 8√2

Another way of solving

We know that

(a + b)² = a² + b² + 2ab

Here

• a + b = 12

• ab = 4

By substituting the values

⇒ 12² = a² + b² + 2(4)

⇒ 144 = a² + b² + 8

⇒ 144 - 8 = a² + b²

⇒ a² + b² = 136

We know that

(a - b)² = a² + b² - 2ab

Here

• a² + b² = 136

• ab = 4

By substituting the values

⇒ (a - b)² = 136 - 2(4)

⇒ (a - b)² = 136 - 8

⇒ (a - b)² = 128

⇒ a - b = √128

⇒ a - b = √64 * √2

⇒ a - b = 8 * √2

⇒ a - b = 8√2

Therefore the value of a - b is 8√2.

Answer 2

Question :

If a+ b = 12 ,ab = 4 , Find a - b

Answer :

The value of a - b = 8√2

Solution :

W . K .T , (a + b)² = a² + b² + 2ab

[Substituting the values ]

${(12)}^{2} = {a}^{2} + {b}^{2} + 2(4)$

$144 = {a}^{2} + {b}^{2} + 8$

$144 - 8 = {a}^{2} + {b}^{2}$

$136 = {a}^{2} + {b}^{2}$

Now ,

As we know ,

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

[Substituting the values ]

${(a - b)}^{2} = 136 - 2(4)$

${(a - b)}^{2} = 136 - 8$

${(a - b)}^{2} = 128$

$a - b = \sqrt{128}$

$a - b = \sqrt{64} \times \sqrt{2}$

$a - b = 8 \sqrt{2}$

Therefore , the value of a - b = 8√2