# 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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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

hope u got the answer :)

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

hope u got the answer :)

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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

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