Question

If a+1 by a =p prove that A3+1by A3 = p (p2-3)

Answer 1

Question :

If a + 1/a = p , then prove that ;

a³ + 1/a³ = p(p² - 3) .

Solution :

• Given : a + 1/a = p
• To prove : a³ + 1/a³ = ?

Proof :

We have ;

a + 1/a = p

Now ,

Cubing both the sides , we get ;

→ (a + 1/a)³ = p³

→ a³ + 1/a³ + 3•a•(1/a)•(a + 1/a) = p³

→ a³ + 1/a³ + 3(a + 1/a) = p³

→ a³ + 1/a³ + 3p = p³

→ a³ + 1/a³ = p³ - 3p

→ a³ + 1/a³ = p(p² - 3)

Hence proved .

Answer 2

⭐ Question ⭐

✏ If a+1 by a =p prove that

a³+1/a³ = p(p²-3)

⭐ Given ⭐

✏ a+1 by a =p

⭐ To Find ⭐

✏ a³+1/a³= ?

⭐ Solution ⭐

✏ (a+1/a) = p

➡ By cubing both side we get,

=> (a+1/a)³ = p³

=> a³+1/a³+3.a.(1/a).(a+1/a) = p³

=> a³+1/a³+3(a+1/a) = p³

=> a³+1/a³+3p = p³

=> a³+1/a³ = p³-3p

=> a³+1/a³ = p(p²-3)

▶ Hence, PROVED ✔

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➡ Important Algebraic Formula:-

1) (a + b)³= a³ + b³ + 3ab(a + b)

2) (a - b)³= a³ - b³ - 3ab(a - b)

3) a³ - b³ = (a - b) (a² + b² + ab)

4) a³+b³ = (a + b) (a² + b² - ab)

5)(a+b+c)³

=a³+b³+c³+3(a+b)(b+c)(c + a)

Step-by-step explanation:

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