Question

if p+1_p=5 find p4+1_p4​

Answer 1

Correct Question :- if (p + 1/p) = 5 , Find the value of (p⁴ + 1/p⁴) == ?

Solution :-

→ (p + 1/p) = 5

Squaring both sides we get,

→ (p + 1/p)² = 5²

Using (a + b)² = a² + b² + 2ab in LHS now,

→ p² + 1/p² + 2 * p * 1/p = 25

→ p² + 1/p² + 2 = 25

→ (p² + 1/p²) = 25 - 2

→ (p² + 1/p²) = 23 .

Now, Squaring Both Sides Again ,

→ (p² + 1/p²)² = (23)²

Again, (a + b)² = a² + b² + 2ab in LHS now,

→ (p²)² + (1/p²)² + 2 * p² * 1/p² = 529

→ (p⁴ + 1/p⁴) = 529 - 2

→ (p⁴ + 1/p⁴) = 527 (Ans) .

Answer 2

Answer:

Step-by-step explanation:

Hey friend !

p+1/p = 5

p⁴+1/p⁴ = ?

p+1/p = 5  Taking these equation and multiplying it with power  4 .

 

(p + 1/p)⁴ = 5⁴

We get :

Once we expand it we get this :

p⁴+1/⁴+4p²+4/p² + 6=625

We can expand 6 into 8-2 and u will know the reason why in the next line!

p⁴+1/⁴+4p²+4/p² +8-2=625

p⁴+1/⁴+4(p²+1/p² + 2 )  - 2=625

U will see that i made it in the form of a square !

p⁴+1/⁴+4(p+1/p)² - 2=625

Now substituting 5 in that place

p⁴+1/p⁴+4 * 5² -2=625

p⁴+1/p⁴ +100-2=625

Now ,

p⁴+1/p⁴ =625 - 98

            = 527

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