Question

A+b= 9 and 1/a+1/b=1/2
find a and b

Answer 1

Answer:

either a=6 then b=3

or a=3 then b=6

Step-by-step explanation:

$a + b = 9(given)$

$\frac{1}{a} + \frac{1}{b} = \frac{1}{2}$

$\frac{a + b}{ab} = \frac{1}{2}$

$putting \: value \: of \: a + b \:we \: get$

$ab = 18$

$b = \frac{18}{a}$

$a + \frac{18}{a} = 9$

${a}^{2} - 9a + 18 = 0$

${a}^{2} - 3a - 6a + 18 = 0$

$a(a - 3) - 6(a - 3) = 0$

$(a - 3)(a - 6) = 0$

$a = 3 \: or \: a = 6$

Now put the values of "a"and simultaneously find the values of "b"

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Answer 2

Answer:

6 and 3

Step-by-step explanation:

    (1/a) + (1/b) = 1/2

=> (b/ab) + (a/ab) = 1/2

=> (a+b)/ab= 1/2

=> 9/ab = 1/2

=> ab = 2 x 9

=> ab = 18

& a+b = 9

Hence, one of them if 6 and other is 3