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Question :

Question:

If (x + 6√2)^(1/2) − (x − 6√2)^(1/2) = 2√2,
then x equals ?

Started 1 day ago by Admin in

0 replies 6 views
Answer : 11

Explanatory Answer

Question:
If (x + 6√2)^(1/2) − (x − 6√2)^(1/2) = 2√2,
then x equals ?

Solution:

Let √(x + 6√2) = a and √(x − 6√2) = b.

Then the given equation becomes:
a − b = 2√2   ...(1)

Also,
a² − b² = (x + 6√2) − (x − 6√2) = 12√2   ...(2)

Now,
a² − b² = (a − b)(a + b)

Substituting (1) and (2):
12√2 = (2√2)(a + b)

⇒ a + b = 6   ...(3)

Now solving (1) and (3):
a − b = 2√2
a + b = 6

Adding: 2a = 6 + 2√2 ⇒ a = 3 + √2
Subtracting: 2b = 6 − 2√2 ⇒ b = 3 − √2

Now,
x + 6√2 = a² = (3 + √2)² = 9 + 2 + 6√2 = 11 + 6√2
⇒ x = (11 + 6√2) − 6√2 = 11

Answer: x = 11

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