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Let (a(1),b(1)) and (a(2),b(2)) are the...

Let `(a_(1),b_(1))` and `(a_(2),b_(2))` are the pair of real numbers such that 10,a,b,ab constitute an arithmetic progression. Then, the value of `((2a_(1)a_(2)+b_(1)b_(2))/(10))` is

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Let `a=10+D " " "……(i)"`
`b=10+2D" " "…..(ii)"`
`ab=10+3D" " "…….(iii)"`
On substituting the values of a and b in Eq. (iii), we get
`(10+D)(10+2D)=(10+3D)`
`implies 2D^(2)+27D+90=0`
`:.d=-6,D=-(15)/(2)`
`:.a_(1)=10-6=4,a_(2)=10-(15)/(2)=(5)/(2)`
and `b_(1)=10-12=-2, b_(2)=10-15=-5`
Now, `((2a_(1)a_(2)+b_(1)b_(2))/(10))=((2xx10+10)/(10))=3`.
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