Question

a+b=27, ab=182 value of a and b

Answer 1

Given :-

$a + b = 27...................(i)$

and


$ab = 182.......................(ii)$


From (ii) we get

$b = \frac{182}{a}$

Putting value of b in (i), we get

$a + \frac{182}{a} = 27 \\ \\ = > a {}^{2} - 27a + 182 = 0 \\ \\ = > a {}^{2} - 14a - 13a + 182 = 0 \\ \\ = > a(a - 14) - 13(a - 14) \\ \\ = > a = 13 \: or \: 14$

a = 13 or 14

b = 14 or 13

Answer 2

hey dear



here is your answer


Given

ab =182


a+b = 27



Now we use identity

( a + b) ^2 = (27)^2


a^2 + b^2 +2ab = 729



a^2 + b^2 = 729 -2ab


a^2 + b^2 = 729 - 2* 182


a^2 + b^2 = 729 -364


a^2 + b^2 = 365


a^2 + b^2 -2ab = 365 -2ab

(a^2 - b^2) = 365 * -2 * 182


a^2 -b^2 = 365 -364


a^2 - b^2 =1


a -b = √1


a-b = +, - 1. ( 2nd equation)


a + b = 27. ( first equation)



Now solving the first and second equation we get



if we take a - b = 1




a+b = 27

a - b =1


a + b +a -b = 27 +1

2a =28

a = 14

as we similarly take a -b = -1


hence b value = 14 -1 =13



hence your answer is a =14 , b = 13



hope it helps


thank you