Question

if (x + 1/x) = 4, find the value of : (x - 1/x)​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given :-

x+(1/x) = 4

To find :-

Find the following :

I) x-(1/x)

ii) x²+(1/x²)

Solution :-

Given that x+(1/x) = 4 ---------(1)

On squaring both sides then

=> [ x+(1/x)]² = 4²

=> x²+2(x)(1/x)+(1/x)² = 16

Since (a+b)² = a²+2ab+b²

Where, a = x and b = 1/x

=> x²+2(x/x) +(1/x²) = 16

=> x²+2(1)+(1/x²) = 16

=> x²+2+(1/x²) = 16

=> x²+(1/x²) = 16-2

=> x²+(1/x²) = 14 ---------------(2)

We know that

(a-b)² = (a+b)² -4ab

On applying this formula to the given problem

=>[x-(1/x)]² = [x+(1/x)]² -4(x)(1/x)

=> [x-(1/x)]² = [x+(1/x)]²-4(x/x)

=> [x-(1/x)]² = [x+(1/x)]²-4(1)

=> [x-(1/x)]² = [x+(1/x)]²-4

=> [x-(1/x)]² = 4²-4

=> [x-(1/x)]² = 16-4

=> [x-(1/x)]² = 12

=> [x-(1/x)] = ±√12

Therefore x-(1/x) = √12 or -√12

Answer :-

I) The value of x-(1/x) = √12 or -√12

II) The value of x²+(1/x²) = 14

Used formulae:-

→ (a+b)² = a²+2ab+b²

→ (a-b)² = (a+b)² -4ab