Question

If X= 1/5-x and X≠ 5 , fing X²-1/x²​

Answer 1

Solution:

Given,

→ x = 1/(5 - x)

We have to find out the value of x² - 1/x²

So, to solve this, we have to find out the values of (x + 1/x) and (x - 1/x).

→ x(5 - x) = 1

→ 5 - x = 1/x

→ x + 1/x = 5 – (i)

Squaring both sides, we get,

→ (x + 1/x)² = 25

→ x² + 1/x² + 2 = 25

Subtracting 4 from both sides, we get,

→ x² + 1/x² + 2 - 4 = 25 - 4

→ (x)² + (1/x)² - 2 × x × 1/x = 21

→ (x - 1/x)² = 21

→ x - 1/x = √21

We omit -√21 because if x is negative, 1/(5 - x) will be positive and so, the equation will not be satisfied.

So,

x² - 1/x²

= (x + 1/x)(x - 1/x)

= 5 × √21

= 5√21 (Answer)

Answer:

• 5√21.

Identity Used:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)

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