Question

If x^2+1/x^2=18 then find the value x-1/x 1) 3 , 2) 8, 3)5, 4) 4

Answer 1

Answer is 4.,,...................

Answer 2

Answer:

Option (4) is correct.

Value of x = 4

Step-by-step explanation:

$Given \:x^{2}+\frac{1}{x^{2}}=18$

/* Subtract $2\times x \times \frac{1}{x}$ both sides of the equation, we get

$x^{2}+\frac{1}{x^{2}}-2\times x \times \frac{1}{x}\\=18-2\times x \times \frac{1}{x}$

$\implies \left(x-\frac{1}{x}\right)^{2}=18-2$

/* By algebraic identity:

a²+b²-2ab = (a-b)² */

$\implies \left(x-\frac{1}{x}\right)^{2}=16$

$\implies \left(x-\frac{1}{x}\right)=±\sqrt{16}$

$x+\frac{1}{x} = ±4$

Therefore,

Value of x = 4

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