Question

If a + 1/a = 5, then a4 + 1/ a4 = ?​

Answer 1

Step-by-step explanation:

given a+1/a=5------eq(1)

on squaring both sides

(a+1/a)^2= a^2+1/a^2+2

(5)^2=a^2+1/a^2+2

25-2= a^2+1/a^2

23= a^2+1/a^2 --------eq(2)

on squaring (eq2) both sides

529= a^4+1/a^4+2

529-2= a^4+1/a^4

therefore a^4+1/a^4 = 527

Answer 2

Correct Question :-

If a + 1/a = 5, then find the value of

$\sf {a}^{4} + \dfrac{1}{{a}^{4} }$

Answer :-

$\sf {a}^{4} + \dfrac{1}{{a}^{4}} = 527$

Solution :-

a + 1/a = 5

Squaring on both sides

(a + 1/a)² = (5)²

⇒ (a + 1/a)² = 25

We know that

(x + y)² = x² + y² + 2xy

Here x = a, y = 1/a

By substituting the values

⇒ (a)² + (1/a)² + 2(a)(1/a) = 25

⇒ a² + 1²/a² + 2 = 25

⇒ a² + 1/a² = 25 - 2

⇒ a² + 1/a² = 23

Squaring on both sides

(a² + 1/a²)² = (23)²

⇒ (a² + 1/a²)² = 529

We know that

(x + y)² = x² + y² + 2xy

Here x = a², y = 1/a²

By substituting the values

⇒ (a²)² + (1/a²)² + 2(a²)(1/a²) = 529

⇒ (a²)² + (1/a²)² + 2 = 529

$\sf \implies {a}^{2(2)} + \dfrac{ {1}^{2} }{( {a}^{2})^{2} } + 2 = 529$

$\sf \implies {a}^{4} + \dfrac{1}{{a}^{2(2)}} + 2 = 529$

$\sf \implies {a}^{4} + \dfrac{1}{{a}^{4}} + 2 = 529$

$\sf \implies {a}^{4} + \dfrac{1}{{a}^{4}} = 529 - 2$

$\sf \implies {a}^{4} + \dfrac{1}{{a}^{4}} = 527$

$\bf \therefore {a}^{4} + \dfrac{1}{{a}^{4}} = 527$