The positive value of λ for which the coefficient of $$x2$$ in the expression $$x2x+$$λ$$x210$$ is $$720$$ is

Question

The positive value of λ for which the coefficient of $$x2$$ in the expression  $$x2x+$$λ$$x210$$ is $$720$$ is

Infinity Learn · Accepted Answer

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 $$x2x+$$λ$$x210$$ $$isTr+1=x2$$ $$10Cr(x)10$$−rλ$$x2r=10Crx2$$⋅$$x10$$−$$r2$$λrx−$$2r=10Cr$$λ$$rx2+10$$−$$r2$$−$$2rNow$$, for the coefficient of $$x2put$$, $$2+10$$−$$r2$$−$$2r=2$$⇒$$10$$−$$r2$$−$$2r=0$$⇒$$10$$−$$r=4r$$⇒$$r=2So$$, the coefficient of $$x2$$ is $$10C2$$λ$$2=720$$⇒    $$10$$!$$2$$!$$8$$!λ$$2=720$$⇒    $$10$$⋅$$9$$⋅$$8$$!$$2$$⋅$$8$$!λ$$2=720$$⇒    $$45$$λ$$2=720$$⇒    λ$$2=16$$⇒λ$$=$$±$$4$$

The positive value of $λ$ for which the coefficient of x² in the expression $x^{2} {(\sqrt{x} + \frac{λ}{x^{2}})}^{10}$ is 720 is

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

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The positive value of $λ$ for which the coefficient of x² in the expression $x^{2} {(\sqrt{x} + \frac{λ}{x^{2}})}^{10}$ is 720 is