Question

if a+b=9 and ab=18 find
(a-b)​

Answer 1

$\huge\mathtt{Hello!}$

$a + b = 9 \: \: \: \: \: ab = 18$

${(a + b)}^{2} = {9}^{2}$

${a}^{2} + {b}^{2} + 2ab = 81$

${a}^{2} + {b}^{2} = 81 - 2(18)$

${a}^{2} + {b}^{2} = 45$

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

$= 45 - 36$

$= 9$

${(a - b)}^{2} = 9$

$a - b = 3$

Answer 2

Question: If a+b=9 and ab=18 find  (a-b)​

Solution:

Given,

(a+b)=9 and ab=18

To find,

(a-b) = ?

Process :-

  $(a+b)^{2} =(9)^{2}$

⇒$a^{2} + b^{2} + 2ab = 81$

⇒$a^{2} +b^{2} + 2(18) = 81$

⇒$a^{2} + b^{2} = 81 - 36$

⇒$a^{2} + b^{2} = 45$

Now,

$(a-b)^{2} = a^{2} +b^{2} -2ab$  $=45- 2(18)$$=45-36$$=9$

Since, $(a-b)^{2} = 9$

Therefore, $(a-b) =$±$\sqrt{9}=$±$3$

Hence, $(a-b) =$±3

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