Find value of (a^2+\sqrt{a^2-1})^4+ (a^2-\sqrt{a^2-1})^4 if a=\sqr | Filo
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Class 11

Math

Algebra

Binomial Theorem

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Find value of $$(a^2+\sqrt{a^2-1})^4+ (a^2-\sqrt{a^2-1})^4$$ if a=$$\sqrt{5}$$.

  1. 2482
Correct Answer: Option(a)
Solution: $$(a^2+\sqrt{a^2-1})^4+ (a^2-\sqrt{a^2-1})^4$$

putting $$a=\sqrt5$$.

$$(\sqrt5^2+\sqrt{\sqrt5^2-1})^4+ (\sqrt5^2-\sqrt{\sqrt5^2-1})^4=(5+\sqrt{5-1})^4+ (5-\sqrt{5-1})^4$$

$$(5+\sqrt{4})^4+ (5-\sqrt{4})^4=(5+2)^4+ (5-2)^4=7^4+3^4=2482$$
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