Question

if a+2b=6and ab=4 then 2/a+1/b=?

Answer 1

a+2b = 6

a = 6-2b --------------(1)

ab = 4 (substitute (1) here)

(6-2b)(b) = 4
6b - 2b² = 4
2b² - 6b +4 = 0 (divide by 2 throughout the eqn.  on both sides)
b² - 3b +2 = 0
b² - 2b - b +2 = 0
b ( b -2 ) -1 ( b - 2 ) = 0
=> (b-1)(b-2) = 0
=> b = 1,2
=> a = 4,2

2/a +1/b = 2/4 +1/1 = 1/2 +1 = 3/2
2/a + 1/b = 2/2 +1/2 = 1 +1/2 = 3/2

Therefore 2/a +1/b = 3/2 in both the cases

Hope it helps!!
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