Find 6 -6-14201-6 -6-14201

The correct option is A 2[^201 C _1(6√(6))^200(14)^1 + ^201 C _3(6√(6))^198(14)^3..............] (6√(6) + 14)^201 = (6√(6))^201 + ^201 C _1(6√(6))^200(14)^1 + ...

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Standard XII

Mathematics

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Find 6 √6-142...

Question

Find $(6 \sqrt{6} - 14)^{201}$ - $(6 \sqrt{6} + 14)^{201}$

2[ $^{201} C_{1}$ $(6 \sqrt{6})^{200}$ $(14)^{1}$ + $^{201} C_{3}$ $(6 \sqrt{6})^{198}$ $(14)^{3}$ ..............]

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2[ $^{201} C_{1}$ $(6 \sqrt{6})^{200}$ $(14)^{1}$ - $^{201} C_{3}$ $(6 \sqrt{6})^{198}$ $(14)^{3}$ ..............]

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2[ $(6 \sqrt{6})^{201}$ + $^{201} C_{2}$ $(6 \sqrt{6})^{199}$ $(14)^{2}$ ..............]

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2[ $(6 \sqrt{6})^{201}$ + $^{201} C_{2}$ $(6 \sqrt{6})^{199}$ $(14)^{2}$ ..............]

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Solution

The correct option is A
2[ $^{201} C_{1}$ $(6 \sqrt{6})^{200}$ $(14)^{1}$ + $^{201} C_{3}$ $(6 \sqrt{6})^{198}$ $(14)^{3}$ ..............]

$(6 \sqrt{6} + 14)^{201}$ = $(6 \sqrt{6})^{201}$ + $^{201} C_{1}$ $(6 \sqrt{6})^{200}$ $(14)^{1}$ + $^{201} C_{2}$ $(6 \sqrt{6})^{199}$ $(14)^{2}$ .............. ............(1)

$(6 \sqrt{6} - 14)^{2 \times 100 + 1}$ = $(6 \sqrt{6})^{201}$ ) - $^{201} C_{1}$ $(6 \sqrt{6})^{200}$ $(14)^{1}$ + $^{201} C_{2}$ $(6 \sqrt{6})^{199}$ $(14)^{2}$ .............. ............(2)

(1) - (2) gives

$(6 \sqrt{6} + 14)^{201}$ - $(6 \sqrt{6} - 14)^{201}$ = 2[ $^{201} C_{1}$ $(6 \sqrt{6})^{200}$ $(14)^{1}$ - $^{201} C_{3}$ $(6 \sqrt{6})^{198}$ $(14)^{3}$ ..............]

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Find (6√6−14)201 - (6√6+14)201

Find $(6 \sqrt{6} - 14)^{201}$ - $(6 \sqrt{6} + 14)^{201}$