Find 3 -3-5 n -3 -3-5 nA- none of the aboveB- 2-3 -3-n-n C23 -3n-252- - - -C- 2-3 -3n-n C23 -3n-252- - -D- 2-n C13 -3n-151-n C33 -3n-353- - -

The correct option is B 2[ + ........................ ] (3√(3) + 5)^n = (3√(3))^n + ^n C _1(3√(3))^n 1(5)^1 + ^n C _2(3√(3))^n 2(5)^2 .................. ...

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Byju's Answer

Standard XII

Mathematics

Properties of Iota

Find 3 √3+5 n...

Question

Find $(3\sqrt{3} + 5)^n$ + $(3\sqrt{3} - 5)^n$

2[ - ........................ ]

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2[ + ........................ ]

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2[ - ........................ ]

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none of the above

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Solution

The correct option is B
2[ + ........................ ]

$(3 \sqrt{3} + 5)^{n}$ = $(3 \sqrt{3})^{n}$ + $^{n} C_{1}$ $(3 \sqrt{3})^{n - 1}$ $(5)^{1}$ + $^{n} C_{2}$ $(3 \sqrt{3})^{n - 2}$ $(5)^{2}$ ...................(1)

$(3 \sqrt{3} - 5)^{n}$ = $(3 \sqrt{3})^{n}$ - $^{n} C_{1}$ $(3 \sqrt{3})^{n - 1}$ $(5)^{1}$ + $^{n} C_{2}$ $(3 \sqrt{3})^{n - 2}$ $(5)^{2}$ ...................(2)

⇒ $(3 \sqrt{3} + 5)^{n}$ + $(3 \sqrt{3} - 5)^{n}$ = 2[ $(3 \sqrt{3})^{n}$ + $^{n} C_{2}$ $(3 \sqrt{3})^{n - 2}$ $(5)^{2}$ ........................ ]

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Find \((3\sqrt{3} + 5)^n\) + \((3\sqrt{3} - 5)^n\)