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Verified answer

Step-by-step explanation:

♦ Given ♦ :-

• (x² + 1)/x = 10/3 , x> 1

♦ To find ♦ :-

• The value of x -(1/x)

♦ Solution ♦ :-

Given equation is (x²+1)/x = 10/3

=> (x²/x)+(1/x) = 10/3

=> x+(1/x) = 10/3

On squaring both sides then

=> [x+(1/x)]² = (10/3)²

=> x²+2(x)(1/x)+(1/x)² = 100/9

Since, (a+b)² = a²+2ab+b²

Where, a = x and b = 1/x

=> x²+2(x/x)+(1/x²) = 100/9

=> x²+(1/x²) +2 = 100/9

=> x²+(1/x²) = (100/9)-2

=> x²+(1/x²) = (100-18)/9

=> x²+(1/x²) = 82/9

Now,

[x-(1/x)]² = x²+(1/x²)-2(x)(1/x)

Since, (a-b)² = a²-2ab+b²

=> [x-(1/x)]² = (82/9)-2(x/x)

=> [x-(1/x)]² = (82/9)-2(1)

=> [x-(1/x)]² = (82/9)-2

=> [x-(1/x)]² = (82-18)/9

=> [x-(1/x)]² = 64/9

=> x-(1/x)= √(64/9)

=> x-(1/x) = 8/3

( since x > 0)

Answer :-

• The value of x-(1/x) is 8/3

Used :-

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