Question

20. If (a+b)=10 and ab=10 then the value of (a-b) is​

Answer 1

Given

❒ a + b = 10

❒ ab = 10

To find

❒ a - b = ?

Solution

This question is completely based on algebraic formulas.

Let's start with what is given..

➜ a + b = 10

❍ Squaring both sides :

➜ (a + b)² = 10²

[Identity : (a + b)² = (a - b)² + 4ab]

➜ (a - b)² + 4ab = 100

➜ (a - b)² + 4 × 10 = 100

➜ (a - b)² = 100 - 40

➜ (a - b)² = 60

➜ a - b = √60

➜ a - b = √(4 × 15)

➜ a - b = 2√15 (Answer)

Therefore, value of (a - b) = 2√15

________________

Some more identities :

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² + b² = (a + b)² - 2ab
• a² + b² = (a - b)² + 2ab
• a² - b² = (a + b)(a - b)
• (a - b)² = (a + b)² - 4ab

Answer 2

$\pink{\bf{\underline{Given:-}}}$

▪$\tt{(a + b) = 10}$

▪$\tt{ab = 10}$

$\purple {\bf {\underline {To\:Find:-}}}$

▪$\tt {The\:value\:of\:(a - b)}$

$\huge\red{\bf {\underline {Solution:-}}}$

$\tt { (a + b) = 10}$

$⇒ \tt{{(a + b)}^{2} = {10}^{2} }$

$⇒ \tt{(a - b)^{2} + 4ab = 100 }$

$⇒ \tt{(a - b)^{2} + 4 \times 10 = 100}$

$⇒ \tt{( {a - b)}^{2} + 40 = 100 }$

$⇒ \tt{(a - b)^{2} = 100 - 40 }$

$⇒ \tt{(a - b)^{2} = 60 }$

$⇒ \tt{a - b = \sqrt{60} }$

$⇒ \tt{a - b = 2\sqrt{15}}$

$\bold\blue {\bf{Hence,\:the\:value\:of\:(a-b)\:is\: 2\sqrt{15}}}$