Question

a2 - 1/a2 = 5, evaluate a4 + 1/a4

Answer 1

(a²-1/a²)=5

whole square both side

(a²-1/a²)²=5²

a⁴+1/a⁴-2×a²×1/a²=25

a⁴+1/a⁴=27

hope its help u....

Answer 2

Correct Question :-

If a² - 1/a² = 5, evaluate $\sf a^4 + \dfrac{1}{a^4}$.

Answer :-

$\tt a^4+ \dfrac{1}{a^4} = 27$

Solution :-

a² - 1/a² = 5

Squaring on both sides

(a² - 1/a²)² = (5)²

⇒ (a² - 1/a²)² = 25

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) = 25

⇒ (a²)² + (1/a²)² - 2 = 25

$\sf \implies a^{2(2)} + \dfrac{ {1}^{2} }{ {( {a}^{2})}^{2} } - 2 = 25$

$\sf \implies a^4+ \dfrac{1}{a^{2(2)}} - 2 = 25$

$\sf \implies a^4+ \dfrac{1}{a^4} - 2 = 25$

Transpose - 2 to RHS [ - 2 becomes 2]

$\sf \implies a^4+ \dfrac{1}{a^4} = 25 + 2$

$\sf \implies a^4+ \dfrac{1}{a^4} = 27$

$\bf \therefore a^4+ \dfrac{1}{a^4} = 27$

Identity used :-

• (x - y)² = x² + y² - 2xy