Question

Find the value of a-b, when a+b=9 and ab=20.

If any of you know the answer to the question, please help me. I want to know the answer to the question ☺️☺️
I have a test for this question tomorrow​

Answer 1

$\red{\large\underline{\sf{Given- }}}$

$\rm :\longmapsto\:a + b = 9$

and

$\rm :\longmapsto\:ab = 20$

$\purple{\large\underline{\sf{To\:Find - }}}$

$\rm :\longmapsto\:a - b$

$\pink{\large\underline{\sf{Solution-}}}$

Given that,

$\rm :\longmapsto\:a + b = 9$

and

$\rm :\longmapsto\:ab = 20$

We know,

$\red{\rm :\longmapsto\:\boxed{\tt{ {(a - b)}^{2} = {(a + b)}^{2} - 4ab}}}$

So, on substituting the values in this identity, we get

$\rm :\longmapsto\: {(a - b)}^{2} = {9}^{2} - 4 \times 20$

$\rm :\longmapsto\: {(a - b)}^{2} = 81 - 80$

$\rm :\longmapsto\: {(a - b)}^{2} =1$

$\bf\implies \:a - b \: = \: \pm \: 1$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

More Identities to know

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)² = (a - b)² + 4ab

(a - b)² = (a + b)² - 4ab

(a + b)² + (a - b)² = 2(a² + b²)

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - b³ - 3ab(a - b)