Question

If a+b=9 a-b then ab=?​

Answer 1

a-b=8

a=8+b…….(1)

ab=9

put value of a in above eq

(8+b)b=9

b²+8b-9=0………..[quad eqn]

i.e b²+9b-b-9=0

b(b+9)-1(b+9)=0

(b-1)(b+9)=0

∴ b-1=0 or b+9=0

b=1 or b=-9

if b=1 then ,

a-b=8

a-1=8

a=8+1

a=9

∴a+b=9+1

a+b=10

and if b=-9 then,

a-b=8

a+9=8

a=8–9

a=-1

∴ a+b=-1–9

a+b=-10

∴ the given problem have two solutions

a+b=10

or

a+b=-10

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