# Find the equation of the line that cuts of intercept a and b on the x and y axis such that a+b=3 and ab =2

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2015-11-29T20:42:25+05:30

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Given
a+b=3 and ab= 2
so, a=2/b
putting in first equation,
2/b+b= 3
⇒2+b²-3b=0
⇒b²-2b-b+2=0
⇒b(b-2)- 1(b-2)=0
⇒(b-2)=0 or (b-1)=0
so,if b=2, a=1 , then equation of line will be 2x+y=2
and if b=1 ,a=2, then equation will be x+2y=2

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2015-11-30T17:18:55+05:30

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Sum of intercept =a+b=3
product of intercept =ab=2
we know that (a-b)²=(a+b)²-4ab
(a-b)²=(3)²-4(2)
(a-b)²=9-8
solving ₁ and ₂
a + b=3
a - b=1
------------
2a   =4
------------
a=4/2 =2
from ₂
a-b=1
2-b=1
2-1=b
b=1
∴ x and y intercept are a=1 , b=2 intercept forms of the line
x/a +y/b =1
x/1 +y/2 =1
2x+y/2 =1
2x+y=2
2x+y-2 =0
if b=1 ,a=2,
x+2y=2
x +2y -2 =0