Suppose k∈R. Let a be the coefficient of the middle term in the expansion of $$kx$$$$+xk10$$, and b be the term independent of x in the expansion of $$k2x+xk10$$. If $$ab=1$$, then k is equal to

Question

Suppose k∈R. Let a be the coefficient of the middle term in the expansion of $$kx$$$$+xk10$$, and b be the term independent of x in the expansion of $$k2x+xk10$$. If $$ab=1$$, then k is equal to

Infinity Learn · Accepted Answer

Middle term of $$kx$$$$+xk10is$$  $$102+1th$$ $$=$$ $$6th$$ term. We have        $$T6=10C5kx10$$−$$5xk3=10C5$$∴ $$a=10C5Also$$, $$(r+1)th$$ term of $$kx$$$$+xk10is$$     $$Tr+1=10Crk2x10$$−$$rxkr=10Crk20$$−$$3rx2r$$−$$10For$$ term independent of x, set $$2r$$−$$10=0$$ or $$r=5$$. Thus, term independent of x in the expansion of $$k2x+xk10is$$  $$10C5k5=b$$.As, $$ab=1$$, we get $$k5=1$$ or $$k=1$$

Suppose $k \in R$ . Let $a$ be the coefficient of the middle term in the expansion of ${(\frac{k}{x} + \frac{x}{k})}^{10},$ and $b$ be the term independent of $x$ in the expansion of ${(\frac{k^{2}}{x} + \frac{x}{k})}^{10} .$ If $\frac{a}{b} = 1,$ then $k$ is equal to

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Suppose k∈R. Let a be the coefficient of the middle term in the expansion of kx+xk10, and b be the term independent of x in the expansion of k2x+xk10. If ab=1, then k is equal to

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Suppose $k \in R$ . Let $a$ be the coefficient of the middle term in the expansion of ${(\frac{k}{x} + \frac{x}{k})}^{10},$ and $b$ be the term independent of $x$ in the expansion of ${(\frac{k^{2}}{x} + \frac{x}{k})}^{10} .$ If $\frac{a}{b} = 1,$ then $k$ is equal to