If a -1- a - p and -0- then a 3-1- a 3 is equal toA- PP2-3B- P2P-3C- p -3D- p p -3

The correct option is A PP2 3Given that a+1/a=p .............. (1) (a+1/a)^3 nbsp;= (a)^3 + (1/a)^3 + 3× a×1/a(a+1/a) (a)^3 + (1/a)^3 = nbsp;(a+1/a)^3 ...

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Byju's Answer

Standard IX

Mathematics

Conditional Identities

If a +1/ a = ...

Question

If $a + \frac{1}{a} = p$ and $a \neq 0$ ; then $a^{3} + \frac{1}{a^{3}}$ is equal to

P (P^{2} - 3)

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P^{2} (P - 3)

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p - 3

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p( p - 3 )

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Solution

The correct option is A $P (P^{2} - 3)$
Given that $a + \frac{1}{a} = p$ .............. (1)

$(a + \frac{1}{a})^{3} = (a)^{3} + (\frac{1}{a})^{3} + 3 \times a \times \frac{1}{a} (a + \frac{1}{a})$

$(a)^{3} + (\frac{1}{a})^{3} = (a + \frac{1}{a})^{3} - 3 (a + \frac{1}{a})$

$(a)^{3} + (\frac{1}{a})^{3} = p^{3} - 3 p$ ........from (1)

$∴$ $(a)^{3} + (\frac{1}{a})^{3}$ = $p (p^{2} - 3)$

Suggest Corrections

Similar questions

Q. If

a + \frac{1}{a} = p

and

a \neq 0

; then show that:

a^{3} + \frac{1}{a^{3}} = p (p^{2} - 3)

State true or false:

a + \frac{1}{a} = p

and

a \neq 0

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a^{3} + \frac{1}{a^{3}} = p (p^{2} - 3)

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If -1+ $\sqrt{- 3}$ =r $e^{i θ}$ , then $θ$ is equal to

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If a+1a=p and a≠0; then a3+1a3 is equal to

The correct option is A P(P2−3)Given that a+1a=p .............. (1) (a+1a)3=(a)3+(1a)3+3×a×1a(a+1a) (a)3+(1a)3=(a+1a)3−3(a+1a) (a)3+(1a)3=p3−3p ........from (1) ∴ (a)3+(1a)3 = p(p2−3)

If $a + \frac{1}{a} = p$ and $a \neq 0$ ; then $a^{3} + \frac{1}{a^{3}}$ is equal to