The positive value of λ for which the coefficient of x2 in the expression  x2x+λx210 is 720 is

The general term in the expansion of binomial expression (a+b)n is Tr+1=nCran−rbrso the general term in the expansion of binomial expression x2x+λx210 isTr+1=x2 10Cr(x)10−rλx2r=10Crx2⋅x10−r2λrx−2r=10Crλrx2+10−r2−2rNow, for the coefficient of x2put, 2+10−r2−2r=2⇒10−r2−2r=0⇒10−r=4r⇒r=2So, the coefficient of x2 is 10C2λ2=720⇒    10!2!8!λ2=720⇒    10⋅9⋅8!2⋅8!λ2=720⇒    45λ2=720⇒    λ2=16⇒λ=±4