Question

pls solve this question..

Answer 1

Answer:

2,-2

Step-by-step explanation:

Given: (5 - 2√6)ˣ + (5 + 2√6)ˣ = 98

⇒ ((5 + 2√6)⁻¹)ˣ + (5 + 2√6)ˣ = 98

⇒ ((5 + 2√6)ˣ)⁻¹ + (5 + 2√6)ˣ = 98

Let 5 + 2√6 = y

⇒ y⁻¹ + y = 98

⇒ (1/y) + y = 98

⇒ 1 + y² = 98y

⇒ y² - 98y + 1 = 0

D = b² - 4ac

   = (-98)² - 4(1)(1)

   = 9600

The solutions are:

x = (-b ± √D)/2a

  = (-98 ± √9600)/2

  = (98 ± 40√6)/2

  = 49 ± 20√6

Now,

(i)

u = 49 + 20√6

⇒ (5 + 2√6)ˣ = 49 + 20√6

⇒ (5 + 2√6)ˣ = (5 + 2√6)²

⇒ x = 2

(ii)

u = 49 - 20√6

⇒ (5 + 2√6)ˣ = (49 - 20√6)

⇒ (5 + 2√6)ˣ = (5 + 2√6)⁻²

⇒ x = -2

Therefore, the values are 2,-2

Hope it helps!

Answer 2

Therefore, the values are 2,-2