The value of -2 - 16 - -2 - 16 will be

(x + a)^n + (x a)^n = 2[x^n + ^n C _2 x^n 2a^2 + ^n C _4 x^n 4a^4 + ^n C _6x^n 6a^6 + .......] Here, n = 6, x = √(2), a = 1; ^6 C _2 = 15, ^6 C _4 = 15, ...

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Standard XII

Mathematics

Binomial Theorem

The value of ...

Question

The value of ${(\sqrt{2} + 1)}^{6}$ + ${(\sqrt{2} - 1)}^{6}$ will be

-198

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198

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-99

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Solution

The correct option is B
198

$(x + a)^{n}$ + $(x - a)^{n}$ = 2 $[x^{n} +^{n} C_{2} x^{n - 2} a^{2} +^{n} C_{4} x^{n - 4} a^{4} +^{n} C_{6} x^{n - 6} a^{6} + . . . . . . .]$

Here, n = 6, x = $\sqrt{2}$ , a = 1;

$^{6} C_{2}$ = 15, $^{6} C_{4}$ = 15, $^{6} C_{6}$ = 1

∴ ( $\sqrt{2} + 1)^{6}$ + ( $\sqrt{2} - 1)^{6}$ = 2 $[(\sqrt{2})^{6} + 15. (\sqrt{2})^{4} .1 + 15 (\sqrt{2})^{2} .1 + 1.1]$

$= 2 [8 + 15 \times 4 + 15 \times 2 + 1] = 198$

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The value of (√2+1)6 + (√2−1)6 will be

The correct option is B 198 (x+a)n + (x−a)n = 2[xn+nC2xn−2a2+nC4xn−4a4+nC6xn−6a6+.......] Here, n = 6, x = √2, a = 1; 6C2 = 15, 6C4 = 15, 6C6 = 1 ∴ (√2+1)6 + (√2−1)6 = 2[(√2)6+15.(√2)4.1+15(√2)2.1+1.1] =2[8+15×4+15×2+1]=198

The value of ${(\sqrt{2} + 1)}^{6}$ + ${(\sqrt{2} - 1)}^{6}$ will be