Question

if x^+1/x^=7 fund the value of x-1/x​

Answer 1

Answer:

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Step-by-step explanation:

Solution:

It is given that x+1/x = 7 ---(1)

(x-1/x)² = (x+1/x)²-2

= 7²-2

= 49-2

= 47

Therefore,

x - 1/x = ± √47

Answer 2

Answer:

$(x - \frac{1}{x}) =$ ±$3\sqrt{5}$

Step-by-step explanation:

Given that:

$x + \frac{1}{x} = 7$  . . . . . . . . . . . . . . .  (i)

$=> (x + \frac{1}{x} )^2 = 7^2$     [Squaring both sides]

$=> x^2 + \frac{1}{x^2} + 2.x.\frac{1}{x} = 49$

$=> x^2 + \frac{1}{x^2} + 2.x.\frac{1}{x} - 4.x.\frac{1}{x} = 49 - 4.x.\frac{1}{x}$  [Subtracting $4.x.\frac{1}{x}$ from both sides]

$=> x^2 + \frac{1}{x^2} - 2.x.\frac{1}{x} = 49 - 4$

$=> (x - \frac{1}{x})^2 = 45$

∴ $(x - \frac{1}{x}) =$ ±$\sqrt{45}=$ ±$3\sqrt{5}$