Question

ab = 8
a^2 + b^2 = 20
Find all values for a and b

Answer 1

Answer:

a=1, b=9

Step-by-step explanation:

1*2+9*20 that is the answer

Answer 2

Answer:

a = 4 and b = 2

Step-by-step explanation:

Given data ab = 8 and  $a^{2} + b^{2}$  = 20

we know that algebraic identities  

$a^{2} + b^{2} + 2ab = ( a+b) ^{2}$   and $a^{2} +b^{2} -2ab = (a-b)^{2}$ by using these identities we will find a and b  

⇒ from given data (a+b)² =  20 + 2(8) = 20 + 16 =36

                               (a+b)² = 36

                                a+b = 6 _(1)             [ 36 = 6² ]  

⇒ (a - b)² = a² + b² - 2ab  = 20 - 2(8)  = 20 -16 =4

                               (a - b)² = 4

                                 a - b = 2 _(2)       [ 4 = 2 ×2 ]    

add (1) and (2) ⇒ a + b + a - b = 6 +2

                       ⇒ 2a = 8

                       ⇒ a = 4

substitute a = 4 in (1) ⇒ 4 + b = 6

                                  ⇒ b = 6 -4 = 2

the values of a and b are 4, 2 respectively