left(x+sqrt{x^{3}-1}right)^{5}+left(x-sqrt{x^ | vedclass

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Question

$(C)$ Since we know that,

${(x+a)^{5}+(x-a)^{5}}$

${=2\left[^{5} C_{0} x^{5}+^{5} C_{2} x^{3} \cdot a^{2}+^{5} C_{4} x \cdot a^{4}\right]}$

$

Vedclass · Accepted Answer

$2$

Vedclass · Answer

$(C)$ Since we know that,

${(x+a)^{5}+(x-a)^{5}}$

${=2\left[^{5} C_{0} x^{5}+^{5} C_{2} x^{3} \cdot a^{2}+^{5} C_{4} x \cdot a^{4}ight]}$

$	herefore \quad(x+\sqrt{x^{3}-1})^{5}+(x-\sqrt{x^{3}-1})^{5}$

$=2\left[^{5} \mathrm{C}_{0} \mathrm{x}^{5}+^{5} \mathrm{C}_{2} \mathrm{x}^{3}\left(\mathrm{x}^{3}-1ight)+^{5} \mathrm{C}_{4} \mathrm{x}\left(\mathrm{x}^{3}-1ight)^{2}ight]$

$\Rightarrow 2\left[x^{5}+10 x^{6}-10 x^{3}+5 x^{7}-10 x^{4}+5 xight]$

$	herefore $ Sum of coefficients of odd degree terms $=2$

$\left(x+\sqrt{x^{3}-1}\right)^{5}+\left(x-\sqrt{x^{3}-1}\right)^{5},(x>1)$ के प्रसार में सभी विषम घातों वाले पदों के गुणांकों का योग है

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